Pengguna:Dedhert.Jr/Uji halaman 01/16: Perbedaan antara revisi
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(30 revisi perantara oleh pengguna yang sama tidak ditampilkan) | |||
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{{distinguish|The Wolf Among Us}} |
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[[Berkas:Logarithm_plots.png|jmpl|300x300px|Grafik fungsi logaritma dengan tiga bilangan pokok yang umum. Titik khusus {{math|<sup>''b''</sup>log ''b'' {{=}} 1}} diperlihatkan oleh garis bertitik, dan semua kurva fungsi memotong di {{math|1=<sup>''b''</sup>log 1 = 0}}.]] |
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{{Operasi aritmetika}} |
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{{Infobox video game|image=Among Us cover art.jpg|alt=Astronot berupa kartun dengan pakaian luar angkasa yang berwarna melayang di luar angkasa. Cahaya terang dan banyaknya bintang terlihat di belakangnya. Di depannya terdapat kata "Among Us", dengan huruf "A" digantikan oleh sebuah astronot berupa kartun.|developer=Innersloth|publisher=Innersloth|released={{Ubl|'''Android, iOS'''|15 Juni 2018|'''Microsoft Windows'''| 16 November 2018<ref>{{Cite web|url=https://store.steampowered.com/app/945360/Among_Us|title = Among Us on Steam}}</ref>|'''Nintendo Switch'''|15 Desember 2020<ref>{{Cite web|url=https://www.nintendo.com/games/detail/among-us-switch/|title=Among Us for Nintendo Switch - Nintendo Game Details}}</ref>|'''PS4, PS5, Xbox One, {{nowrap|Xbox Series X/S}}'''|14 Desember 2021<ref>{{Cite web|url=https://www.innersloth.com/xbox-playstation-launch-on-dec-14/|title = Xbox & PlayStation launch on Dec 14! 🚀 | Innersloth - Creators of Among Us and the Henry Stickmin Collection!}}</ref>}}|platforms={{Ubl|[[Android (operating system)|Android]]|[[iOS]]|[[Microsoft Windows]]|[[Nintendo Switch]]|[[PlayStation 4]]|[[PlayStation 5]]|[[Xbox One]]|[[Xbox Series X/S]]}}|modes=[[Permainan video pemain jamak|Pemain jamak]]|genre={{hlist|[[Permainan video pesta|Pesta]]|[[Permainan deduksi sosial|deduksi sosial]]}}|programmer=Forest Willard{{Efn|name=fortebass|Better known as "ForteBass".<ref name=":7" />}}|designer=Marcus Bromander{{Efn|name=puffballs|Better known as "PuffballsUnited".<ref name=":3" />}}|artist={{ubl|Marcus Bromander{{Efn|name=puffballs}}|Amy Liu}}|engine=[[Unity (game engine)|Unity]]|title=Among Us|caption=Gambar sampul}}'''''Among Us'''''{{Efn|Saat membahas tentang sekuelnya yang direncanakan, permainan ini diberikan sebuah [[retronim|nama baru]], yaitu '''''Among Us 1''''', oleh pengembang permainan video beserta beberapa berita yang disalurkan.<ref name="sequelannouncement"/><ref name="gamerantsequel"/><ref name="techraptorsequel"/><ref name="sequelsomag"/>|name=|group=}} adalah sebuah [[Permainan video pemain jamak|permainan pemain jamak daring]] dan [[Permainan deduksi sosial|deduksi sosial]] tahun 2018 yang dikembangkan dan dipublikasikan oleh studio permainan asal [[Amerika Serikat]], Innersloth. Permainan ini terinspirasi oleh sebuah permainan pesta ''[[Mafia (permainan pesta)|Mafia]]'' dan film horor bertemakan fiksi ilmiah, ''[[The Thing (1982 film)|The Thing]]''. Video permainan ini tersedia untuk [[permainan lintas platform]] seperti perangkat [[iOS]] dan [[Android (operating system)|Android]] yang pertama kali dirilis pada Juni 2018 dan di [[Microsoft Windows|Windows]] pada bulan November 2018. Kemudian video permainan ini diporta ke [[Nintendo Switch]] pada Desember 2020, dan di [[PlayStation 4]], [[PlayStation 5]], [[Xbox One]] dan [[Xbox Series X/S]] pada Desember 2021. Pada saat video permainan ini dirilis pada tahun 2018 dan menarik perhatiannya sedikit, permainan tersebut mendapatkan peningkatan popularitas yang sangat besar pada tahun 2020. Hal ini dikarenakan adanya banyak para streamer Twitch dan para [[YouTuber]] yang memainkannya. Sebuah permainan video versi VR yang dikembangkan oleh [[Schell Games]], ''Among Us VR'', akan dirilis untuk [[Meta Quest 2|Quest 2]], [[SteamVR]], dan [[PlayStation VR]]. |
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Dalam [[matematika]], '''logaritma''' merupakan [[fungsi invers]] dari [[eksponensiasi]]. Dengan kata lain, logaritma suatu nilai {{mvar|x}} merupakan [[eksponen]] dengan [[Bilangan pokok (eksponen)|bilangan pokok]] {{mvar|b}} yang dipangkatkan dengan bilangan sesuatu agar memperoleh nilai {{mvar|x}}. Kasus sederhana dalam logaritma menghitung jumlah munculnya faktor yang sama dalam perkalian berulang. Sebagai contoh, {{math|1000 {{=}} 10 × 10 × 10 {{=}} 10<sup>3</sup>}} dibaca, "logaritma 1000 dengan bilangan pokok 10 sama dengan 3" atau dinotasikan sebagai {{math|<sup>10</sup>log (1000) {{=}} 3}}. Logaritma dari {{mvar|x}} dengan ''bilangan pokok'' {{mvar|b}} dilambangkan {{math|<sup>''b''</sup>log ''x''}}. Terkadang logaritma dilambangkan sebagai {{math|log<sub>''b''</sub> (''x'')}} atau tanpa menggunakan tanda kurung. {{math|log<sub>''b''</sub> ''x''}}, atau bahkan tanpa menggunakan bilangan pokok, {{math|log ''x''}}. |
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''Among Us'' mengambil latar tempat yang bertemakan [[Science fiction|luar angkasa]], dimana para pemain terlihat seperti [[astronot]] berupa kartun, tanpa tangan, dan berwarna. Namun semenjak peta [[wahana antariksa]] "The Skeld" dirilis, tiga peta lainnya telah ditambahkan pada tahun sebelumnya seperti: menara puncak "MIRA HQ", pangkalan planet "Polus", dan "The [[Airship]]" (yang berasal dari serial ''Henry Stickmin'', ''Infiltrating the Airship'', juga dikembangkan oleh Innersloth). Masing-masing pemain memainkan salah satu dari dua peran (hampir semua yang diperankan adalah ''crewmate'', namun ada jumlah sedikit pemain yang memerankan sebagai ''impostor'') sehingga tidak dapat mengubah penampilannya.{{Efn|Permainan video ini menggunakan ejaan kata bahasa Inggris dalam "Impostor", bukan "Imposter" (meskipun kedua ejaan kata tersebut benar).<ref>{{cite web |last1=King |first1=Austin |title=Among Us Impostor vs. Imposter: Why InnerSloth Spells It Different |url=https://screenrant.com/among-us-impostor-imposter-innersloth-spelling-different-why/ |website=ScreenRant |access-date=April 9, 2021 |date=January 18, 2021}}</ref>}} Tujuan ''crewmate'' adalah mengidentifikasi dan melakukan pemungutan suara agar para ''Impostor'' dikeluarkan, atau menyelesaikan semua tugas-tugas di sekitar peta; sedangkan tujuan ''impostor'' adalh menyabotase misi para ''crewmate'' secara diam-diam dengan membunuh mereka sebelum mereka menyelesaikan tugasnya atau dengan memicu bencana yang tidak dapat mengatasinya. |
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Ada tiga bilangan pokok logaritma yang umum beserta kegunaannya. Logaritma bilangan pokok {{math|10}} ({{math|1=''b'' = 10}}) disebut sebagai [[logaritma umum]], yang biasanya dipakai dalam ilmu sains dan rekayasa. Adapun [[logaritma alami]] dengan bilangan pokok [[E (konstanta matematika)|bilangan {{Math|''e''}}]] ({{math|''b'' ≈ 2.718}}), yang dipakai dengan luas dalam matematika dan fisika karena dapat mempermudah perhitungan [[integral]] dan [[turunan]]. Adapula [[logaritma biner]] menggunakan bilangan pokok {{math|2}} ({{math|1=''b'' = 2}}), yang seringkali dipakai dalam [[ilmu komputer]]. |
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== Alur permainan ==<!-- In this image, white does not have a red name because the screenshot is from the Among Us trailer, made before Impostors had red names. --> |
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Logaritma diperkenalkan oleh [[John Napier]] pada tahun 1614 sebagai alat yang menyederhanakan perhitungan.<ref>{{citation|url=http://archive.org/details/johnnapierinvent00hobsiala|title=John Napier and the invention of logarithms, 1614; a lecture|last=Hobson|first=Ernest William|date=1914|publisher=Cambridge : University Press|others=University of California Libraries}}</ref> Logaritma dipakai lebih cepat dalam navigator, ilmu sains, rekayasa, ilmu ukur wilayah, dan bidang lainnya untuk lebih mempermudah perhitungan nilai yang sangat akurat. Dengan menggunakan [[Tabel matematika|tabel logaritma]], cara yang membosankan dalam mengalikan digit yang banyak dapat digantikan dengan melihat tabel dan penjumlahan yang lebih mudah. Ini dapat dilakukan karena bahwa logaritma dari [[Darab (matematika)|hasil kali]] bilangan merupakan logaritma dari [[Penjumlahan|jumlah]] faktor bilangan: |
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[[Berkas:AmongUsWhiteKillBlue.png|al=A white-suited astronaut named "Buddy" (the player) stands in front of an unnamed blue-suited corpse. The room they are in is labeled "Admin". In the hallway, slightly obscured by the sight line mechanic, is a pink-suited astronaut named "Chum". In the upper-left corner of the player's screen, there is a fake list of tasks as well as the player's goal: to kill all Crewmates. The player also has the option to Use, Report, Sabotage, and Kill. As the player has just killed, the button is on cooldown and faded.|kiri|jmpl|282x282px|Pada cuplikan gambar berikut mengenai alur permainan dari peta aslinya, The Skeld, ''impostor'' berawrna putih baru saja membunuh ''crewmate'' berwarna biru di tengah-tengah ruang Admin. Karena mekanik pandangan ''Among Us'', pemain berwarna pink terlihat sebagian dalam daerah pandangan pemain berwarna putih. Setiap pemain dapat melaporkan adanya mayat dan memicu pertemuan.]]<!-- # of players and maps --> |
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''Among Us'' merupakan sebuah [[permainan video pemain jamak]] yang berjumlahkan empat hingga limabelas pemain (versi sebelumnya berjumlahkan empat hingga sepuluh pemain), meskipun jumlah minimumnya direkomendasi setidaknya lima pemain.<ref name=":29">{{Cite web|last=Innersloth|date=June 15, 2021|title=Among Us' 3rd Birthday & 15 Player Lobbies! - Among Us by Innersloth|url=https://innersloth.itch.io/among-us/devlog/261573/among-us-3rd-birthday-15-player-lobbies|website=[[itch.io]]|access-date=June 16, 2021}}</ref> Pemain yang berjumlahkan tiga dipilih secara acak<ref>{{cite web|author=Izaak|date=September 29, 2020|title=Is there a surefire way to become an imposter in Among Us?|url=https://www.sportskeeda.com/esports/news-how-become-impostor-among-us|website=[[Sportskeeda]]|access-date=December 30, 2020}}</ref> dan secara diam-diam menjadi ''impostor'' pada setiap babak. Hingga pada tahun 2021, babak permainan dapat mengambil tempat pada salah satu dari empat [[Level (permainan video)|peta]]: peta wahana antariksa yang disebut "The Skeld"; gedung kantor pusat yang disebut "MIRA HQ"; pangkalan planet yang disebut "Polus";<ref name=":6" /> atau peta bertemakan pesawat luar angkasa yang disebut "The Airship" (yang berasal dari serial Innersloth, ''Henry Stickmin'').<ref name=":31">{{cite web|last=Chalk|first=Andy|date=March 31, 2021|title=The newest Among Us map, The Airship, is now live|url=https://www.pcgamer.com/among-us-map-the-airship-live/|work=[[PC Gamer]]|access-date=March 31, 2021}}</ref><ref name=":32">{{Cite web|last=Innersloth|date=March 31, 2021|title=LET'S GO AIRSHIP 🎉 New update out now! – Among Us by Innersloth|url=https://innersloth.itch.io/among-us/devlog/237019/lets-go-airship-new-update-out-now|website=[[Itch.io]]|access-date=April 4, 2021}}</ref><!-- win conditions -->Pemain berperan sebagai ''impostor'' menang melalui salah satu dari dua cara berikut: dengan membunuh seluruh awak (hingga jumlahnya sama dengan jumlah ''impostor'') atau dengan melakukan sabotase sistem kritikal pada peta (asalkan c''rewmate'' tidak mengatasinya dengan waktu yang tepat). Dengan demikian, para ''crewmate'' dapat memenangkan babak melalui salah satu dari dua cara berikut: dengan menyelesaikan semua tugas atau dengan mengidentifikasikan dan mengeluarkan semua ''impostor'' melalui pemungutan suara.<ref name=":6" /> Permainan juga dapat diakhiri bila para pemain keluar dari babak jika dilakukan untuk memenuhi setiap kondisi agar menang (misalnya jika ''crewmate'' keluar dari permainan, maka tugas ''crewmate'' secara otomatis dianggap selesai).<ref>{{Cite web|last=Duckworth|first=Joshua|date=October 8, 2020|title=Among Us: 5 Quality of Life Improvements The Game Needs|url=https://gamerant.com/among-us-5-imposter-ghosts-penalties-cheating-quality-life-improvements/|website=Game Rant|language=en-US|access-date=October 18, 2020}}</ref><ref>{{Cite web|last=Mc|first=Chris|date=October 2, 2020|title=How to Find the Impostor in Among Us|url=https://www.gamespew.com/2020/10/eighteen-tips-for-beating-the-impostor-in-among-us/|website=GameSpew|language=en-GB|access-date=October 18, 2020}}</ref><ref name=":2" /><!-- abilities --> |
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Pada saat permainan dimulai, ''crewmate'' diberi misi untuk menyelesaikan "tugas" (berupa [[minigame]], [[Puzzle|minipuzzle]], dan menekan tombol sederhana) di sekitar peta, meskipun hampir semua tugas memelihara sistem yang penting seperti memperbaiki kabel dan mengunduh data;<ref name=":1" /> sedangkan ''impostor'' diberi daftar tugas palsu untuk berbaur dengan para ''crewmate''. Akan tetapi, impostor tidak dapat mengerjakan tugas dan hanya dapat berpura-pura mengerjakan setiap tugas di dalam pesawat tersebut, serta impostor dapat menyabotase sistem penting (seperti pasokan oksigen di peta The Skeld), menutup pintu ruangan, berjalan diam-diam dan dengan cepat melalui sistem ventilasi, dan membunuh para ''crewmate'' ketika berdiri di dekatnya. Agar membantu para ''crewmate'' menemukan identitas ''impostor'', ada beberapa [[Pengawasan|sistem pengawasan]] pada masing-masing peta, seperti [[kamera keamanan]] dan sistem [[Sysadmin|admin]] dalam peta The Skeld,<ref name=":20" /> pintu masuk dengan banyaknya sensor dalam peta MIRA HQ,<ref>{{Cite web|last=Stella|first=Marloes|date=September 25, 2020|title=Among Us Guide: tips to winning as Crewmates|url=https://www.pcgamesn.com/among-us/guide-tips|website=[[PCGamesN]]|language=en-GB|archive-url=https://web.archive.org/web/20200927151252/https://www.pcgamesn.com/among-us/guide-tips|archive-date=September 27, 2020|access-date=September 26, 2020|url-status=live}}</ref> dan indikator penting dalam peta Polus.<ref name=":6" /> Para ''crewmate'' juga dapat mengkonfirmasi identitasnya melalui "tugas-tugas yang dapat dilihat" (seperti tugas yang mempunyai animasi ketika dimainkan pemain lain), sehingga para ''impostor'' tidak dapat memalsukannya.<ref>{{Cite web|last=Meluso|first=Maria|date=October 20, 2020|title=Every Visible Task in Among Us (& How They Work)|url=https://screenrant.com/every-visible-task-among-us-how-to-complete/|website=ScreenRant|language=en-US|access-date=November 8, 2020}}</ref><!-- ghosts -->Jika sebuah ''crewmate'' dibunuh atau setiap pemain dikeluarkan, maka mereka menjadi hantu. Hantu dapat melewati dinding, melihat aktivitas pemain lain, serta melihat dan mengirim pesan dengan hantu lainnya.<ref name=":2" /> Pemain yang masih hidup mempunyai [[Kabut perang#Dalam permainan video|pandangan terbatas yang berbentuk kerucut]],<ref name=":5" /> sedangkan hantu tidak mempunyainya.<ref>{{Cite web|last=Paez|first=Danny|date=September 16, 2020|title=3 'Among Us' ghost tips to help your team win from beyond the grave|url=https://www.inverse.com/gaming/among-us-ghost-tips-how-to-win-crewmate-imposter-ejection|website=[[Inverse (website)|Inverse]]|language=en|archive-url=https://web.archive.org/web/20200921123215/https://www.inverse.com/gaming/among-us-ghost-tips-how-to-win-crewmate-imposter-ejection|archive-date=September 21, 2020|access-date=September 16, 2020|url-status=live}}</ref> Terlebih lagi, para hantu tidak dapat berbicara dengan atau dilihat oleh pemain yang masih hidup. Para hantu (sebagai ''crewmate'') membantu rekan-rekannya yang masih hidup dengan menyelesaikan tugasnya atau (sebagai ''impostor'') melakukan berbagai tindakan berupa sabotase.<ref name=":6" /><!-- meetings --> |
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: <math> \log_b(xy) = \log_b x + \log_b y,</math> |
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Setiap pemain dapat memanggil pertemuan kelompok dengan melaporkan adanya mayat, atau dengan menekan tombol "pertemuan darurat" dalam peta kapan saja (kecuali saat terjadi sabotase di bagian utamanya, ketika "pertemuan darurat" tidak dapat dipanggil, namun masih bisa melaporkan adanya mayat).<ref name=":2" /><ref name=":0" /><ref>{{Cite web|last=Marshall|first=Cass|date=September 18, 2020|title=New Among Us players keep accidentally outing themselves as aliens|url=https://www.polygon.com/2020/9/18/21445675/among-us-community-memes-new-players-accidental-guilt|website=[[Polygon (website)|Polygon]]|language=en|archive-url=https://web.archive.org/web/20200921123249/https://www.polygon.com/2020/9/18/21445675/among-us-community-memes-new-players-accidental-guilt|archive-date=September 21, 2020|access-date=September 19, 2020|url-status=live}}</ref> Selama pertemuan berlangsung, pemain berdiskusi siapakah yang dipercayai berdasarkan [[bukti-bukti]] tersedia. Para ''impostor'' dapat diidentifikasi diluar [[Dugaan yang wajar|dugaan]] bila mereka telah melakukan ''venting'' ataupun membunuh. Pemain dapat dicurigai karena ada banyak alasan lainnya. Namun, semua pemain membentuk semacam [[juri]] dan harus mempertimbangkan kejujuran ataupun nilai dari pernyataan setiap pemain lainnya dan bertanya saat melakukan pertemuan. [[Pemungutan suara kemajemukan|Pemungutan suara]] dilakukan secara bersama, dan jika pemain memperoleh suara, maka yang mendapatkan pemungutan para ''crewmate'' terbanyak dikeluarkan dari peta dan menjadi hantu, kecuali sebagian besar para ''crewmate'' memilih untuk melewati pemungutan atau ketika pemungutannya seri.<ref name=":1" /><ref name=":2" /> Pemain dapat berkomunikasi melalui can [[Obrolan daring|obrolan teks]] (dengan ada beberapa frasa yang belum dijelaskan bagi pengguna ponsel),<ref name=":1" /> namun hanya dilakukan saat pertemuan, dan hanya jika pemain hidup (walaupun hantu dapat berbicara dengan yang lain kapanpun).<ref name=":6" /><ref name=":2" /><ref name=":5" /> Sementara bagi permainan yang tidak mempunyai sistem [[Obrolan suara dalam permainan daring|obrolan suara]], pemain biasanya menggunakan program luar seperti [[Discord (perangkat lunak)|Discord]],<ref name=":8" /><ref name=":9" /><ref name=":10" /> atau tetap sebaliknya jika para pemain tetap dekat dengan pemain yang lain. Jika para pemain mendengar suara setiap pemain lainnya, permainan tersebut mengingatkan mereka untuk tidak berbicara kecuali saat pertemuan. |
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asalkan bahwa {{mvar|b}}, {{mvar|x}} dan {{mvar|y}} bilangan positif dan {{math|''b'' ≠ 1}}. [[Kaidah geser]] yang juga berasal dari logaritma dapat mempermudah perhitungan tanpa menggunakan tabel, namun perhitungannya kurang akurat. [[Leonhard Euler]] mengaitkan gagasan logaritma saat ini dengan [[fungsi eksponensial]] pada abad ke-18, dan juga memperkenalkan huruf {{mvar|e}} sebagia bilangan pokok logaritma alami.<ref>{{citation|title=Theory of complex functions|last=Remmert, Reinhold.|date=1991|publisher=Springer-Verlag|isbn=0387971955|location=New York|oclc=21118309}}</ref> |
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Pada November 2021, ada beberapa peran tambahan yang tersedia bagi para pemain yang memperluas selain peran berupa Crewmate atau Impostor. ''Crewmate'' juga dapat menjadi Engineers ({{Lang-id|Ahli rekayasa}}), Scientists ({{Lang-id|Ilmuwan}}), atau Guardian Angels ({{Lang-id|Malaikat penjaga}}). Para ''engineer'' mengizinkan para ''crewmate'' untuk menjelajah melalui ventilasi seperti hal yang dapat dilakukan oleh ''impostor'', <u>albeit to a limited capacity</u>. Scientists can check vitals at any time to see if any player has been killed recently. Crewmates who become Ghosts can become Guardian Angels, which can temporarily protect living players from being killed. Impostors likewise can be Shapeshifters, allowing them to temporarily morph into other players.<!-- customizable options -->In each game's lobby, various options can be adjusted to customize aspects of gameplay, such as player movement speed, the allowed number of emergency meetings, number of tasks, if there will be "visual tasks",<ref name=":4" /> or whether or not an Impostor is revealed after being voted off.<ref>{{Cite news|last=Garst|first=Aron|title=Playing "Among Us?" Here are some tips and alternate rules to up the ante.|url=https://www.washingtonpost.com/video-games/tips/among-us-tips-rules/|newspaper=[[The Washington Post]]|language=en-US|issn=0190-8286|access-date=October 9, 2020}}</ref> There are also many cosmetic options, including spacesuit colors, [[Skin (video gaming)|skins]], hats, and pets,<ref>{{Cite magazine|last=Wilde|first=Tyler|date=September 24, 2020|title=How to customize your character in Among Us|url=https://www.pcgamer.com/how-to-customize-your-character-in-among-us/|url-status=live|archive-url=https://web.archive.org/web/20200927112805/https://www.pcgamer.com/how-to-customize-your-character-in-among-us/|archive-date=September 27, 2020|access-date=September 28, 2020|magazine=[[PC Gamer]]|language=en-US}}</ref><ref name=":19" /> some of which are paid [[downloadable content]].{{Efn|Both the free mobile version of ''Among Us'' and the paid PC version have paid DLC. For the PC version, however, some of the mobile version's DLC is included in the standalone game.<ref>{{Cite web|first=Zackery|last=Cuevas|date=October 2, 2020|title=All the differences between the PC and mobile versions of Among Us|url=https://www.androidcentral.com/there-difference-between-pc-and-mobile-versions-among-us|access-date=October 2, 2020|website=[[Android Central]]|archive-date=October 13, 2020|archive-url=https://web.archive.org/web/20201013043233/https://www.androidcentral.com/there-difference-between-pc-and-mobile-versions-among-us|url-status=live}}</ref><ref name=":7" />|name=|group=}}<ref name=":7" /><ref name="gamerantsequel" /><ref name=":5" /> |
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[[Skala logaritma]] mengurangi jumlah luas ke lingkup yang lebih kecil. Misalnya, [[desibel]] (dB) adalah [[Satuan pengukuran|satuan]] yang digunakan untuk menyatakan [[Tingkat (kuantitas logaritmik)|rasio sebagai logaritma]], sebagian besar untuk kekuatan sinyal dan amplitudo (contoh umumnya pada [[tekanan suara]]). Dalam kimia, [[pH]] mengukur [[Asam|keasaman]] dari [[larutan berair]] melalui logaritma. Logaritma biasa dalam [[rumus]] ilmiah, dan dalam pengukuran [[Teori kompleksitas komputasi|kompleksitas algoritma]] dan objek geometris yang disebut [[fraktal]]. Logaritma juga membantu untuk menjelaskan [[frekuensi]] rasio [[Interval (musik)|interval musik]], muncul dalam rumus yang menghitung [[bilangan prima]] atau [[Hampiran Stirling|hampiran]] [[faktorial]], memberikan gambaran dalam [[psikofisika]], dan dapat membantu perhitungan [[akuntansi forensik]]. |
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== Pengembangan dan perilisan == |
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Konsep logaritma sebagai invers dari eksponensiasi juga memperluas ke struktur matematika lain. Namun pada umumnya, logaritma cenderung merupakan fungsi bernilai banyak. Sebagai contoh, [[logaritma kompleks]] merupakan [[Fungsi invers|invers]] dari fungsi eksponensial pada [[bilangan kompleks]]. Mirip contoh lain, [[logaritma diskret]] dalam grup hingga, merupakan invers fungsi eksponensial bernilai banyak yang memiliki kegunaan dalam [[kriptografi kunci publik]]. |
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=== Awal pengembangan === |
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{{Video game timeline|||title=''Among Us'' release timeline for various platforms|range1=2018|range2=2019|range3=2020|range4=2021|range5=Akan diumumkan|2018a=iOS/Android|2018b=Windows|2019a="MIRA HQ"|2019b="Polus"|2020a=[[Nintendo Switch]]|2021a="The Airship"|2021b=[[PlayStation 4]], [[PlayStation 5]], [[Xbox One]] and [[Xbox Series X/S]]|TBA=''Among Us VR''}}''Among Us'' terinspirasi oleh [[permainan pesta]] live ''[[Mafia (permainan pesta)|Mafia]]'',<ref name=":7" /><ref name=":16" /> dan film [[Horror fiksi ilmiah|horror bertemakan fiksi ilmiah]], [[The Thing (1982 film)|''The Thing'']].<ref name=":33">{{Cite web|last=Fischer|first=Tyler|date=January 9, 2021|title=Original Among Us Was a Much Different and More Stressful Game|url=https://comicbook.com/gaming/news/among-us-game-original/|website=Comicbook|language=en|access-date=February 1, 2021}}</ref> Ide konsep permainan video ini berasal dari seorang pendiri Innersloth, Marcus Bromander, yang telah memainkan ''Mafia'' semenjak ia masih kanak-kanak. In the original game, function cards were dealt and players wandered around a house, aimlessly, while another person secretly killed the players, drawing a finger around their neck. Most of its mechanics were still present in ''Among Us'', but the team wanted to "alleviate the need to create an interesting home model and have someone wandering around in a boring environment". So, they decided that the game would be space themed and also added tasks, which, according to Forest Willard, programmer at Innersloth, "changed several times during development".<ref name=":33" /><ref name=":28">{{Cite web|date=January 9, 2021|title=Among Us dev recounts how the game took flight, including early game ideas|url=https://indieworld.nintendo.com/news/#among-us-dev-recounts-how-the-game-took-flight|website=Nintendo|access-date=February 9, 2021}}</ref> |
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[[Berkas:Binary_logarithm_plot_with_grid.png|alt=Grafik memperlihatkan kurva logaritmik yang melintasi sumbu-''x'' di {{math|''x''= 1}} dan mendekati negatif takhingga di sepanjang garis sumbu-''y''.|ka|jmpl|Gambar memperlihatkan [[Grafik fungsi|grafik]] logaritma dengan bilangan pokok 2 memotong [[Sistem koordinat Cartesius|sumbu-''x'']] di {{math|''x'' {{=}} 1}} dan melalui titik {{nowrap|(2, 1)}}, {{nowrap|(4, 2)}}, dan {{nowrap|(8, 3)}}, sebagai contoh, {{math|log<sub>2</sub>(8) {{=}} 3}} dan {{math|2<sup>3</sup> {{=}} 8}}. Grafik tersebut dengan sembarang mendekati sumbu--{{mvar|y}}, but [[Asymptotic|does not meet it]].]] |
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Operasi aritmetika yang paling dasar adalah [[penambahan]], [[perkalian]], dan [[Eksponensiasi|eksponen]]. Kebalikan dari penambahan adalah [[pengurangan]], dan kebalikan dari perkalian adalah [[pembagian]]. Mirip contoh sebelumnya, logaritma merupakan kebalikan dari operasi [[eksponesiasi]]. Eksponensiasi adalah sebuah bilangan ''bilangan pokok'' {{mvar|b}} yang ketika dipangkatkan dengan {{mvar|y}} memberikan nilai {{mvar|x}}. Ini dirumuskan sebagai |
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Pengembangan ''Among Us'' dimulai pada November 2017.<ref name=":28" /> Permainan video ini pada awalnya bertujuan untuk menjadikannya sebuah permainan [[Permainan video pemain jamak|multipemain lokal]] dengan satu peta yang hanya dimainkan di ponsel .<ref name="improb" /> Bromander menghentikan pengembangan permainan Innersloth lainnya, ''The Henry Stickmin Collection'', yang bertujuan untuk membangun peta pertama permainan ''Among Us'', The Skeld.<ref name="newgroundspod">{{Cite web|title=#27 – Innersloth|url=https://www.newgrounds.com/audio/listen/972286|language=en|access-date=October 20, 2020}}</ref> Ketika memulai pengembangan peta pertamanya, <u>they intended that the ship was always in crisis and that the Impostors could do tasks</u>. However, they found this setup "stressful" and decided that it "[wouldn't leave] much time for detective work and informed meeting conversations".<ref name=":33" /><ref name=":28" /> Willard described [[Playtest|playtesting]] as painful and frustrating, as the game would break down during sessions forcing him to send playtesters new builds off of [[Google Play]]. The team tested the game with 8 of their friends and never tested the game with 9 or the maximum of 10 players.<ref name="newgroundspod" /> The game was developed using the [[Unity (game engine)|Unity]] engine.<ref name="itchpage" /> |
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: <math>b^y=x.</math> |
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The game was released in June 2018 to [[Android (operating system)|Android]] and [[iOS]] under the AppID of "spacemafia".<ref name=":7" /><ref>{{Cite web|title=Among Us – Apps on Google Play|url=https://play.google.com/store/apps/details?id=com.innersloth.spacemafia&hl=en_US|website=[[Google Play]]|language=en|archive-url=https://web.archive.org/web/20200921123231/https://play.google.com/store/apps/details?id=com.innersloth.spacemafia&hl=en_US|archive-date=September 21, 2020|access-date=September 13, 2020|url-status=live}}</ref> Shortly after release, ''Among Us'' had an average player count of 30 to 50 concurrent players.<ref name=":4" /> Bromander blamed the game's poor release on Innersloth being "really bad at marketing".<ref name="improb" /> The team nearly abandoned the project multiple times, but continued work on it due to a "small but vocal player base",<ref name=":14" /> adding in online multiplayer, new tasks, and customization options.<ref name=":14" /> The game was released on [[Steam (service)|Steam]] on November 16, 2018.<ref name="improb" /><ref name="outofbeta" /> [[Cross-platform play]] was supported upon release of the Steam version.<ref>{{Cite web|last=Power|first=Tom|date=September 16, 2020|title=Is there crossplay in Among Us?|url=https://www.gamepur.com/guides/is-there-crossplay-in-among-us|website=Gamepur|language=en-US|archive-url=https://web.archive.org/web/20200924153020/https://www.gamepur.com/guides/is-there-crossplay-in-among-us|archive-date=September 24, 2020|access-date=September 21, 2020|url-status=live}}</ref><ref>{{Cite magazine|last=Matthews|first=Emma|date=September 10, 2020|title=How crossplay works in Among Us|url=https://www.pcgamer.com/among-us-crossplay-pc-and-mobile/|access-date=September 15, 2020|magazine=[[PC Gamer]]|language=en-US|archive-date=September 21, 2020|archive-url=https://web.archive.org/web/20200921123342/https://www.pcgamer.com/among-us-crossplay-pc-and-mobile/|url-status=live}}</ref> Originally, the game had no audio to avoid revealing hidden information in a local setting,{{Efn|For example, the sound of an Impostor killing a Crewmate could reveal to other Crewmates who the Impostor was.|name=|group=}} and Willard mixed sounds from numerous sound packs to compose the SFX during the game's Steam release.<ref name="newgroundspod" /> |
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Sebagai contoh, {{math|2}} pangkat {{math|3}} memberikan nilai {{math|8}}. Secara matematis, <math>2^3 = 8</math>. |
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On August 8, 2019, Innersloth released a second map, MIRA HQ,<ref name=":11" /><ref>{{Cite web|last=InnerSloth|date=August 8, 2019|title=MIRA HQ Launched! – Among Us by Innersloth|url=https://innersloth.itch.io/among-us/devlog/94023/mira-hq-launched|website=[[Itch.io]]|language=en|archive-url=https://web.archive.org/web/20200921123251/https://innersloth.itch.io/among-us/devlog/94023/mira-hq-launched|archive-date=September 21, 2020|access-date=September 16, 2020|url-status=live}}</ref> a "tightly packed headquarters roughly the size of The Skeld." A third map, Polus, was added on November 12, 2019, and is set in a research station.<ref name=":11" /><ref>{{Cite web|last=Innersloth|date=November 12, 2019|title=Polus Map Launched! – Among Us by InnerSloth|url=https://innersloth.itch.io/among-us/devlog/109603/polus-map-launched|website=[[Itch.io]]|language=en|archive-url=https://web.archive.org/web/20200921123255/https://innersloth.itch.io/among-us/devlog/109603/polus-map-launched|archive-date=September 21, 2020|access-date=September 16, 2020|url-status=live}}</ref> The fourth map, the Airship, was released on March 31, 2021, and is based on a location in the ''Henry Stickmin'' universe.<ref name=":31" /><ref name=":32" /> MIRA HQ and Polus originally cost players {{Currency|4}} via in-app purchase. Their prices were reduced to {{Currency|2}} on January 6, 2020, then made free on June 11, 2020.<ref>{{cite web|last=Innersloth|date=January 6, 2020|title=Among Us and Innersloth in 2020 – Among Us by Innersloth|url=https://innersloth.itch.io/among-us/devlog/118224/among-us-and-innersloth-in-2020|website=[[Itch.io]]|language=en|archive-url=https://web.archive.org/web/20200924212833/https://innersloth.itch.io/among-us/devlog/118224/among-us-and-innersloth-in-2020|archive-date=September 24, 2020|access-date=September 27, 2020|url-status=live}}</ref> While the map packs are still available for purchase on all platforms, they now only provide the player the skins that were bundled with the maps.<ref>{{cite web|date=June 11, 2020|title=Among Us – All Maps Free and Among Us Merch! – Steam News|url=https://store.steampowered.com/newshub/app/945360/view/2406558942705547209|website=[[Steam (service)|Steam]]|language=en|archive-url=https://web.archive.org/web/20200926165007/https://store.steampowered.com/newshub/app/945360/view/2406558942705547209|archive-date=September 26, 2020|access-date=September 27, 2020|url-status=live}}</ref> According to programmer Forest Willard, the team "stuck with [the game] a lot longer than we probably should have from a pure business standpoint", putting out regular updates to the game as often as once per week. This led to a steady increase in players, causing the game's player base to [[Snowball effect|snowball]]. Bromander attributed this to the studio having enough savings to keep working on the game even while it was not selling particularly well.<ref name="improb" /> |
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Logaritma dengan bilangan pokok {{mvar|b}} merupakan operasi invers yang menyediakan nilai keluar {{mvar|y}} dari nilai masukan {{mvar|x}}. Dalam artian, <math>y = \log_b x</math> ekuivalen dengan to <math>x=b^y</math> jika {{mvar|b}} [[bilangan real]] positif. (Jika {{mvar|b}} bukanlah bilangan real positif, eksponensiasi dan logaritma dapat didefinisikan, namun memberikan beberapa nilai, sehingga definisi darinya semakin rumit.) |
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=== Sekuel yang dibatalkan dan pembaruan yang terus berlanjut === |
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Salah satu alasan bersejarah utamanya dalam memperkenalkan logaritma adalah rumus |
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In August 2020, the team shifted focus onto a sequel, ''Among Us 2''.<ref name="sequelannouncement" /><ref name="gamerantsequel" /><ref name="techraptorsequel" /><ref name="sequelsomag" /> During this time, Forest Willard and Amy Liu continued to update ''Among Us'', increasing the maximum player base, adding four servers and three regions,<ref>{{cite web|last=Willard|first=Forest|date=September 1, 2020|title=Among Us Beta 2020.9.1 :: Among Us General Discussions|url=https://steamcommunity.com/app/945360/discussions/0/2923353981937819321/|website=[[Steam (service)|Steam]] Community|language=en|archive-url=https://web.archive.org/web/20200921123256/https://steamcommunity.com/app/945360/discussions/0/2923353981937819321/|archive-date=September 21, 2020|access-date=September 18, 2020|url-status=live}}</ref> and implementing longer multiplayer codes to support more concurrent games.<ref>{{cite web|last=Willard|first=Forest|date=September 10, 2020|title=Servers Update (2020.9.9 beta) :: Among Us General Discussions|url=https://steamcommunity.com/app/945360/discussions/0/2952628643857359158/|website=[[Steam (service)|Steam]] Community|language=en|archive-url=https://web.archive.org/web/20200921123256/https://steamcommunity.com/app/945360/discussions/0/2952628643857359158/|archive-date=September 21, 2020|access-date=September 18, 2020|url-status=live}}</ref> On September 23, 2020, the team canceled the sequel, instead opting to add all content intended for the sequel to the original ''Among Us'', due to "how many people [were] enjoying [the original game]".<ref name=":13" /><ref name=":15" /><ref name=":12">{{cite web|last=Innersloth|date=September 23, 2020|title=The Future of Among Us|url=https://innersloth.itch.io/among-us/devlog/181107/the-future-of-among-us|website=[[Itch.io]]|archive-url=https://web.archive.org/web/20200924084429/https://innersloth.itch.io/among-us/devlog/181107/the-future-of-among-us|archive-date=September 24, 2020|access-date=September 23, 2020|url-status=live}}</ref> However, Innersloth deemed the game's [[codebase]] "outdated and not built to support adding so much new content", so the team made plans to rework the game's core code to enable adding new features.<ref name=":12" /> The team subsequently announced their plans to fix the game's server issues and widespread [[Cheating in online games|cheating]] problem,<ref name=":24">{{Cite web|last=Grayson|first=Nathan|date=October 2, 2020|title=Among Us Has A Cheating Problem|url=https://kotaku.com/among-us-has-a-cheating-problem-1845256959|website=[[Kotaku]]|language=en-us|archive-url=https://web.archive.org/web/20201003212735/https://kotaku.com/among-us-has-a-cheating-problem-1845256959|archive-date=October 3, 2020|access-date=October 4, 2020|url-status=live}}</ref><ref name=":25">{{Cite web|last=Marshall|first=Cass|date=October 8, 2020|title=Among Us with randoms is rough|url=https://www.polygon.com/2020/10/8/21499102/amoung-us-playing-game-popularity-random-public-lobbies|website=[[Polygon (website)|Polygon]]|language=en|archive-url=https://web.archive.org/web/20201009025656/https://www.polygon.com/2020/10/8/21499102/amoung-us-playing-game-popularity-random-public-lobbies|archive-date=October 9, 2020|access-date=October 9, 2020|url-status=live}}</ref><ref name=":26">{{Cite magazine|last=Wilde|first=Tyler|date=October 5, 2020|title=Of course there are already Among Us cheaters|url=https://www.pcgamer.com/of-course-there-are-already-among-us-cheaters/|url-status=live|archive-url=https://web.archive.org/web/20201009115036/https://www.pcgamer.com/of-course-there-are-already-among-us-cheaters/|archive-date=October 9, 2020|access-date=October 9, 2020|magazine=[[PC Gamer]]|language=en-US}}</ref> as well as add a system for banning disruptive players.<ref name=":21">{{Cite web|last=Turney|first=Alexandria|date=October 9, 2020|title=Everything Among Us Desperately Needs To Add|url=https://screenrant.com/among-us-voice-chat-report-filter-new-maps/|website=[[Screen Rant]]|language=en-US|archive-url=https://web.archive.org/web/20201013144959/https://screenrant.com/among-us-voice-chat-report-filter-new-maps/|archive-date=October 13, 2020|access-date=October 13, 2020|url-status=live}}</ref> In October 2020, [[Color blindness|colorblind]] support for the "wires" task was added to the ''Among Us'' [[Beta development stage|beta]] on Steam, as well as some previously unannounced lobby customization options.<ref>{{Cite web|last=Kent|first=Emma|date=October 12, 2020|title=Among Us beta adds new ways to spice up investigations|url=https://www.eurogamer.net/articles/2020-10-12-among-us-beta-adds-new-ways-to-spice-up-investigations|website=Eurogamer|language=en|archive-url=https://web.archive.org/web/20201013075055/https://www.eurogamer.net/articles/2020-10-12-among-us-beta-adds-new-ways-to-spice-up-investigations|archive-date=October 13, 2020|access-date=October 13, 2020|url-status=live}}</ref><ref>{{Cite web|last=Wheelock|first=Kyle|date=October 13, 2020|title=Among Us Beta Updates Make Both Impostors' & Crewmates' Jobs Easier|url=https://screenrant.com/among-us-beta-updates-impostors-crewmates-tasks-easier/|website=[[Screen Rant]]|language=en-US|archive-url=https://web.archive.org/web/20201015160731/https://screenrant.com/among-us-beta-updates-impostors-crewmates-tasks-easier/|archive-date=October 15, 2020|access-date=October 13, 2020|url-status=live}}</ref> As-of-yet unimplemented features include a fifth map, the Sheriff role, and new game modes.<ref name=":13" /><ref name=":15" /><ref name=":21" /><ref name=":35">{{Cite magazine|last=Hetfeld|first=Malindy|date=May 21, 2021|title=Among Us teases new crewmate colour ahead of 'next big update' announcement this June|url=https://www.pcgamer.com/among-us-teases-new-crewmate-colour-ahead-of-next-big-update-arriving-june/|access-date=May 25, 2021|magazine=[[PC Gamer]]}}</ref><ref name=":36">{{Cite web|last=J. Teuton|first=Christopher|date=June 10, 2021|title=Among Us New Map & Hide and Seek Mode Revealed At Summer Games Fest|url=https://screenrant.com/among-us-hide-seek-new-map-achievements-colors/|website=[[Screen Rant]]|access-date=June 14, 2021}}</ref> |
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In mid-February 2021, the game added a feature called Quickchat, which replaces the standard chat interface with a series of preset phrases that players must pick from. Players under the age of 13 are required to use Quickchat, but those over 13 are also allowed to use Free Chat, which allows them to type original messages.<ref>{{Cite web|date=2021-03-08|title=What Among Us' New Quickchat Feature Is (& What It Does)|url=https://screenrant.com/among-us-quickchat-wheel-new-feature-works-how/|website=ScreenRant|language=en-US|access-date=2021-04-25}}</ref><ref>{{Cite news|date=2021-03-08|title=Among Us introduces quick chat option that's "faster and safer"|url=https://www.rockpapershotgun.com/among-us-quick-chat-feature-update|work=Rock Paper Shotgun|language=en|access-date=2021-04-25}}</ref> First announced at [[The Game Awards 2020]], the Airship map was released on March 31, 2021.<ref name=":31" /><ref name=":32" /> The Airship features multiple floors, contraptions, tasks, and "more".<ref>{{Cite web|last=Team|first=M. G. H.|date=December 11, 2020|title=Among Us 'The Airship' Map: Release Date, Leaks, Costumes and More|url=https://mobilegaminghub.com/2020/12/12/among-us-the-airship-map-release-date-leaks-costumes-and-more/|website=Mobile Gaming Hub|language=en-US|access-date=December 11, 2020}}</ref><ref>{{Cite web|last=Adler|first=Matthew|date=November 19, 2020|title=Among Us Teases New Airship Map|url=https://www.ign.com/articles/among-us-teases-new-map-with-boat-theme|website=IGN}}</ref> In addition, Game Awards presenter [[Geoff Keighley]]'s face was added as a skin. The map itself is based upon the ''Henry Stickmin'' series's Toppat Clan Airship.<ref>{{Cite web|last=Skrebels|first=Joe|date=December 11, 2020|title=Among Us Reveals New Map, The Airship|url=https://sea.ign.com/news/167007/among-us-reveals-new-map-the-airship|website=[[IGN]] Southeast Asia|publisher=[[Ziff Davis]]|language=en-sg|access-date=December 14, 2020}}</ref> Innersloth also stated that the map would be free to all players.<ref>{{Cite web|last=Innersloth|date=November 3, 2020|title=Small Patch and Small Roadmap – Among Us by Innersloth|url=https://innersloth.itch.io/among-us/devlog/192737/small-patch-and-small-roadmap|website=[[Itch.io]]|access-date=March 15, 2021}}</ref><ref name=":32" /> It also features a skin bundle that includes ''Henry Stickmin''-themed cosmetic that can be bought on Steam.<ref name=":32" /> |
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: <math>\log_b(xy)=\log_b x + \log_b y,</math> |
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The accounts system was implemented along with the update, and it allows players to report players that are not following Innersloth's Code of Conduct in order to make the game a welcoming and respectful place. Punishment ranges from temporary to a permanent ban. They also stated that reports would be viewed manually and not by bots, that account creations would be required if players want to use Free Chat or to customize their nicknames, and that people under the age of 13 would need their parents' permission to create an account. Implementing an account system also allowed Innersloth to add account linking and a friending system in future updates.<ref>{{Cite web|last=Holt|first=Kris|date=March 24, 2021|title=The upcoming 'Among Us' account system is mostly about making the game safer|url=https://www.engadget.com/among-us-account-system-safety-harassment-kids-185830761.html|website=Engadget|access-date=March 25, 2021}}</ref><ref>{{Cite web|last=Innersloth|date=March 24, 2021|title=Info on Accounts – Among Us by Innersloth|url=https://innersloth.itch.io/among-us/devlog/235010/info-on-accounts|website=[[Itch.io]]|access-date=March 25, 2021}}</ref> Innersloth later revealed on the game's official Twitter account a new color to the game, Rose, which was included in the game's next update along with five other colors: Coral, Tan, Gray, Maroon, and Banana, which were revealed during Summer Game Fest on June 10, 2021, alongside other upcoming content, including a fifth map, new Hide & Seek game mode, and new roles such as Sheriff and Scientist.<ref name=":35" /><ref name=":36" /> The new colors, along with 15 player lobby support, new meeting screen and revamp at the game's design, was released on June 15, 2021, during the game's 3rd anniversary.<ref name=":29" /> |
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yang dapat mempermudah perhitungan nilai perkalian dan pembagian dengan penjumlahan, pengurangan, dan melihat [[tabel logaritma]]. Perhitungan ini ditemukan sebelum adanya penemuan komputer. |
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== Definisi == |
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''Logarithm'' suatu bilangan real positif {{mvar|x}} terhadap bilangan pokok {{mvar|b}}{{refn|Perbatasan {{mvar|x}} dan {{mvar|b}} dijelaskan pada bagian [[#Sifat analitik|"Sifat analitik"]].|group=nb}} merupakan eksponen dengan bilangan pokok {{mvar|b}} yang dipangkatkan suatu bilangan agar memperoleh nilai {{mvar|x}}. Dengan kata lain, logaritma bilangan pokok {{mvar|b}} dari {{mvar|x}} merupakan bilangan real {{mvar|y}} sehingga <math>b^y = x</math>.<ref>{{Citation|last1=Kate|first1=S.K.|last2=Bhapkar|first2=H.R.|title=Basics Of Mathematics|location=Pune|publisher=Technical Publications|isbn=978-81-8431-755-8|year=2009|url={{google books |plainurl=y |id=v4R0GSJtEQ4C|page=1}}}}, chapter 1</ref> Logaritma dilambangkan sebagai {{math|<sup>''b''</sup>log ''x''}} (dibaca "logaritma {{mvar|x}} dengan bilangan pokok {{mvar|b}}"). Adapun definisi yang setara dan lebih ringkasnya mengatakan bahwa fungsi {{math|<sup>''b''</sup>log}} [[Fungsi invers|invers]] dengan fungsi <math>x\mapsto b^x</math>. |
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On July 7, 2021, Innersloth released a minor update that adds a new task, "Clean Vent", which involves the Crewmate cleaning a specific vent, preventing Impostors from using it.<ref>{{Cite web|title=Among Us July 7 Patch Notes: New Vent Cleaning Task, Bug Fixes|url=https://www.gamespot.com/articles/among-us-july-7-patch-notes-new-vent-cleaning-task-bug-fixes/1100-6493670/|website=GameSpot|language=en-US|access-date=2021-07-07}}</ref> On November 9, 2021, a major update was released that introduced four new roles, achievements, a level system, controller support, custom keybinds, visor cosmetics, cosmetic bundles called "Cosmicubes", various in-game currencies, and a major revamp to the in-game store.<ref>{{cite web|last1=Stanton|first1=Rich|date=November 10, 2021|title=Big Among Us update adds four new roles, an XP system, and multiple currencies|url=https://www.pcgamer.com/big-among-us-update-adds-four-new-roles-an-xp-system-and-multiple-currencies|website=PC Gamer|access-date=November 20, 2021}}</ref> On March 31, 2022, a friending system was added, which allows players to see who they recently played with, send and receive friend requests, send and receive lobby invites, as well as the ability to block people.<ref>{{cite web|date=March 31, 2022|title=Among Us on Twitter|url=https://twitter.com/AmongUsGame/status/1509579445916471297|access-date=April 21, 2022}}</ref> |
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Sebagai contoh, {{math|1=<sup>2</sup>log 16 = 4}}, karena {{math|1=2<sup>4</sup> = 2 × 2 × 2 × 2 = 16}}. Logaritma juga berupakan nilai negatif, sebagai contoh <math display="inline">\log_2 \! \frac{1}{2} = -1</math>, karena <math display="inline">2^{-1} = \frac{1}{2^1} = \frac{1}{2}</math>. Logaritma juga berupa nilai desimal, sebagai contoh {{math|<sup>10</sup>log 150}} kira-kira sama dengan 2.176, karena terletak di antara 2 dan 3, begitu pula 150 terletak antara {{math|1=10<sup>2</sup> = 100}} dan {{math|1=10<sup>3</sup> = 1000}}. Adapun sifat logaritma bahwa untuk setiap {{mvar|b}}, {{math|1=<sup>''b''</sup>log ''b'' = 1}} karena {{math|1=''b''<sup>1</sup> = {{mvar|b}}}}, dan {{math|1=<sup>''b''</sup>log 1 = 0}} karena {{math|1=''b''<sup>0</sup> = 1}}. |
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During [[The Game Awards 2021]], ''Among Us VR'' was announced for [[SteamVR]], [[PlayStation VR]], and the [[Meta Quest 2]], developed by [[Schell Games]].<ref>{{Cite web|last=Valentine|first=Rebekah|date=December 9, 2021|title=Among Us Vents Into VR|url=https://www.ign.com/articles/among-us-vents-vr|website=IGN}}</ref> During the Meta Quest Showcase on April 20, 2022, an aproximate release date was officially announced, with the game coming out around the holidays of 2022.<ref>{{cite web|date=April 20, 2022|title=Holiday 2022. Happy, purple?|url=https://twitter.com/AmongUsVR/status/1516826803201003523|website=Twitter|access-date=April 21, 2022}}</ref> |
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== Identitas logaritma == |
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{{Main|Daftar identitas logaritma}} |
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Ada beberapa rumus penting, terkadang disebut ''identitas logaritma'', mengaitkan logaritma dengan yang lainnya.<ref>Semua pernyataan di bagian ini dapat ditemukan pada {{Harvard citations|last1=Shirali|first1=Shailesh|year=2002|loc=bagian 4|nb=yes}}. Sebagai contoh, {{Harvard citations|last1=Downing|first1=Douglas|year=2003|loc=hlm. 275}}, atau {{Harvard citations|last1=Kate|last2=Bhapkar|year=2009|loc=hlm. 1-1|nb=yes}}.</ref> |
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=== Perilisan konsol === |
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=== Hasil kali, hasil bagi, pangkat, dan akar === |
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Amid its popularity, Innersloth considered releasing the game to [[PlayStation 4]] and [[Xbox One]] consoles, but encountered a problem in implementing player communication, since standard text-based or voice-based chat seemed unusable. They considered a system similar to the "quick comms" system from ''[[Rocket League]]'', as well as the possibility of developing an entirely new communication system for the game.<ref name=":8" /><ref name=":9" /> Versions of the game for Xbox consoles were later announced.<ref>{{Cite web|date=2021-02-06|title=Here's everything you need to know about Among Us for Xbox|url=https://www.windowscentral.com/among-us-xbox|website=Windows Central|access-date=2021-04-20}}</ref> |
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Logaritma suatu hasil kali merupakan jumlah logaritma dari bliangan yang dikalikan dan logaritma hasil bagi dari dua bilangan merupakan selisih logaritma. Logaritma dari bilangan pangkat ke-{{Mvar|p}} sama dengan ''{{Mvar|p}}'' dikali logaritma itu sendiri dan logaritma bilangan akar ke-{{Mvar|p}} sama dengan logaritma dibagi dengan {{Mvar|p}}. Berikut adalah tabel yang memuat daftar sifat-sifat logaritma tersebut beserta conohtnya. Masing-masing identitas ini berasal dari hasil substitusi dari definisi logaritma <math>x = b^{\, ^b\!\log x}</math> atau <math>y = b^{\, ^b\!\log y}</math> pada ruas kiri. |
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{| class="wikitable" style="margin: 0 auto;" |
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! |
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!Rumus |
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!Contoh |
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|- |
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|Hasil kali |
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|<math display="inline">\log_b(x y) = \log_b x + \log_b y</math> |
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|<math display="inline">\log_3 243 = \log_3 (9 \cdot 27) = \log_3 9 + \log_3 27 = 2 + 3 = 5</math> |
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|- |
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|Hasil bagi |
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|<math display="inline">\log_b \!\frac{x}{y} = \log_b x - \log_b y</math> |
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|<math display="inline">\log_2 16 = \log_2 \!\frac{64}{4} = \log_2 64 - \log_2 4 = 6 - 2 = 4</math> |
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|- |
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|Pangkat |
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|<math display="inline">\log_b\left(x^p\right) = p \log_b x</math> |
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|<math display="inline">\log_2 64 = \log_2 \left(2^6\right) = 6 \log_2 2 = 6</math> |
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|- |
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|Akar |
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|<math display="inline">\log_b \sqrt[p]{x} = \frac{\log_b x}{p}</math> |
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|<math display="inline">\log_{10} \sqrt{1000} = \frac{1}{2}\log_{10} 1000 = \frac{3}{2} = 1.5</math> |
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|} |
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''Among Us'' was released for the [[Nintendo Switch]] on December 15, 2020, the same day it was announced during [[Nintendo Direct]] [[Indie World]] showcase. The Switch version supports cross-platform play with the mobile and Windows versions.<ref>{{Cite web|last=Farokhmanesh|first=Megan|date=December 15, 2020|title=Among Us launches for the Nintendo Switch today|url=https://www.theverge.com/2020/12/15/22176459/among-us-nintendo-switch-cross-play-launch|website=[[The Verge]]|language=en|access-date=December 15, 2020}}</ref> This port was published by Play EveryWare.<ref name=":30">{{Cite web|last=Innersloth|date=March 18, 2021|title=📣 March 31 – The Airship Releases! – Among Us by Innersloth|url=https://innersloth.itch.io/among-us/devlog/232933/-march-31-the-airship-releases|website=[[Itch.io]]|access-date=March 20, 2021}}</ref> Upon release, the Switch version had an [[Video game exploit|exploit]] to access ''The Airship'' prior to its official release in early 2021.<ref>{{Cite web|last=Lee|first=Julia|date=December 16, 2020|title=How to play Among Us' new Airship map on Nintendo Switch|url=https://www.polygon.com/2020/12/16/22179208/among-us-new-map-airship-nintendo-switch|website=[[Polygon (website)|Polygon]]|language=en|access-date=December 23, 2020}}</ref> The exploit was fixed two days after release in the Switch version's first update.<ref>{{Cite web|author=rawmeatcowboy|date=December 20, 2020|title=Among Us Airship map glitch fixed|url=https://gonintendo.com/stories/374458-among-us-airship-map-glitch-fixed|website=gonintendo.com|language=en|access-date=December 23, 2020}}</ref><ref>{{Cite web|date=December 21, 2020|title=List of Nintendo Switch game patches/updates|url=http://www.benoitren.be/switch-gamepatches.html|website=benoitren.be|language=en|archive-url=https://archive.today/20201223200717/http://www.benoitren.be/switch-gamepatches.html|archive-date=December 23, 2020|access-date=December 23, 2020|url-status=live}}</ref> |
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=== Mengubah bilangan pokok ===<!-- This section is linked from [[Mathematica]] --> |
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Logaritma {{math|<sup>''b''</sup>log ''x''}} dapat dihitung sebagai hasil bagi logaritma {{mvar|x}} dengan logaritma {{mvar|b}} terhadap bilangan pokok sembarang {{Mvar|k}}. Secara matematis dirumuskan sebagai: |
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''Among Us'' was released digitally for PlayStation 4, [[PlayStation 5]], Xbox One and [[Xbox Series X/S]] consoles on December 14, 2021, along with its release on the [[Xbox Game Pass]] for console. These versions will support cross-platform play with existing Windows, Switch, and mobile versions. Unique to the PlayStation ports are special customization options based on ''[[Ratchet & Clank]]''. Physical releases for consoles will be available in Europe the same day, while North American physical releases will be available in January 2022.<ref>{{cite web|last=Warren|first=Tom|date=October 21, 2021|title=Among Us is coming to Xbox, PlayStation, and Xbox Game Pass on December 14th|url=https://www.theverge.com/2021/10/21/22738583/among-us-xbox-playstation-game-pass-release-date|work=[[The Verge]]|access-date=October 21, 2021}}</ref> |
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: <math> \log_b x = \frac{\log_k x}{\log_k b}.\, </math> |
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{{Collapse top|title=Bukti perubahan antara logaritma dengan bilangan pokok sembarang|width=80%}} |
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Pada identitas |
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=== Peretasan pada Oktober 2020 dan Januari 2021 === |
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: <math> x = b^{\log_b x} </math> |
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Pada pertengahan Oktober 2020, seorang peretas bernama "Eris Loris" mulai menyerang sebagian besar server Amerika Utara. Ada beberapa pemain di [[Reddit#Subreddit|subreddit]] dan [[Twitter]] ''Among Us'' melaporkan bahwa pemain ini meretas lobinya dan melakukan [[spam]] dalam obrolan permainan berupa promosi kanal YouTube-nya, pranala server Discord, dan pesan berupa politik yang bersifat kontroversial.<ref>{{Cite web|last=Mukherjee|first=Arnab|date=October 24, 2020|title=Among Us Hacker: Who is Eris Loris & how to respond to his Among Us hack /spam attack – guide|url=https://thesportsrush.com/among-us-hacker-who-is-eris-loris-how-to-respond-to-his-among-us-hack-spam-attack-guide/|website=The SportsRush|language=en-US|access-date=October 25, 2020}}</ref> Eris Loris juga mengancam kepada pemain peretas secara pribadi bagi yang menolak untuk berlangganan dengan kanal YouTube-nya. Serber Discordnya yang telah ditemukan mengandung sejumlah unsur yang bersifat menyerang, seperti kata-kata rasis, mengandung unsur darah, pornografi dan gambar penyalahgunaan hewan.<ref name=":22">{{Cite web|last=Emma|first=Kent|date=October 23, 2020|title=Among Us is dealing with a huge spam attack|url=https://www.eurogamer.net/articles/2020-10-23-among-us-is-dealing-with-a-huge-spam-attack|website=[[Eurogamer]]|language=en-Us|archive-url=https://web.archive.org/web/20201024215004/https://www.eurogamer.net/articles/2020-10-23-among-us-is-dealing-with-a-huge-spam-attack|archive-date=October 24, 2020|access-date=October 24, 2020|url-status=live}}</ref> |
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Laporan kanal Youtube bernama ''Eurogamer'' pada 23 Oktober 2020 menampilkan wawancara dengan seorang yang bernama Eris Loris. Wawancara tersebut diadakan melalui server Discord dari salah satu tautan yang tersedia dalam permainan yang diretas. Dalam wawancara, Loris mengklaim bahwa ia menciptakan bot yang bertanggunjawab atas peretasannya "hanya dalam enam jam", <u>and had enlisted up to 50 volunteers to form a [[botnet]] which boosted the strength of their attacks</u>. Loris mengklaim bahwa peretasan yang ia lakukan memberikan dampak terhadap 4,9 juta pemain dalam 1,5 juta permainan. Ia juga menambah bahwa peretasan tersebut merupakan bagian dari aksi publik yang bertujuan agar membujuk pemain untuk memilih [[Donald Trump]] sebagai presiden Amerika Serikat dalam [[Pemilihan presiden Amerika Serikat 2020|pemilu tahun 2020]].<ref name=":22" /> |
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dapat menerapkan {{math|<sup>''k''</sup>log}}pada kedua ruas sehingga memperoleh |
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Innersloth menambahkan sebuah pesan dalam permainannya berupa peringatan kepada pemain mengenai peretasan yang terjadi pada 22 Oktober,<ref name=":22" /> dan merilis sebuah pernyataan di Twitter pada keesokan harinya. Innersloth mengatakan bahwa mereka harus "sangat berhati-hati" terhadap masalah berupa peretasan, dan mengatakan bahwa "pembaruan server darurat" would be pushed out to combat the hacks. They encouraged players to stick to private games and to avoid playing on public ones until the update was released.<ref name=":23">{{Cite web|last=Innersloth|date=October 23, 2020|title=Innersloth's Response to the hacking problem|url=https://twitter.com/InnerslothDevs/status/1319471920115376130|website=[[Twitter]]|language=en-US|archive-url=https://web.archive.org/web/20201024234001/https://twitter.com/InnerslothDevs/status/1319471920115376130|archive-date=October 24, 2020|access-date=October 24, 2020|url-status=live}}</ref> The team plans to address the hacking vulnerabilities as part of a planned overhaul for the game.<ref name=":24" /><ref name=":25" /><ref name=":26" /> At the end of January 2021, players reported on Twitter the return of Eris Loris' hack attack, which is now distributing ''Among Us'' cheats.<ref name="EirsLorisWave2">{{Cite web|last1=Khan|first1=Aqdas|date=January 30, 2021|title=Eris Loris Among Us : "Another hack wave?", Players ask questions as Eris Loris hack is reportedly back|url=https://thesportsrush.com/eris-loris-among-us-another-hack-wave-players-ask-questions-as-eris-loris-hack-is-reportedly-back/|website=The Sports Rush|language=en-US|access-date=February 7, 2021}}</ref> |
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: <math> \log_k x = \log_k \left(b^{\log_b x}\right) = \log_b x \cdot \log_k b</math>. |
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== Popularitas == |
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Mencari solusi untuk <math>\log_b x</math> menghasilkan persamaan: |
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=== Naiknya popularitas pada tahun 2020 === |
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: <math> \log_b x = \frac{\log_k x}{\log_k b}</math>, |
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[[Berkas:Sodacrop.png|al=Sodapoppin in a purple Twitch hoodie|ka|jmpl|[[Streamer (video gaming)|Streamer]] [[Sodapoppin]] is credited with popularizing ''Among Us'' on the live-streaming platform [[Twitch (service)|Twitch]].]] |
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While ''Among Us'' released in 2018, it was not until mid-2020 that it saw a surge of popularity, initially driven by content creators online in South Korea and Brazil. Bromander stated that the game is more popular in Mexico, Brazil, and South Korea than the United States.<ref name="improb" /><ref name=":7" /> According to Willard, [[Twitch (service)|Twitch]] streamer [[Sodapoppin]] first popularized the game on Twitch in July 2020.<ref name="improb" /> Many other Twitch streamers and YouTubers followed suit, including prominent content creators [[xQc]], [[Pokimane]], [[Shroud (gamer)|Shroud]], [[Ninja (gamer)|Ninja]], [[Disguised Toast]] and [[PewDiePie]].<ref name=":15" /><ref>{{Cite web|last=Zheng|first=Jenny|date=September 21, 2020|title=Among Us Is Even More Popular Than You Think Right Now|url=https://www.gamespot.com/articles/among-us-is-even-more-popular-than-you-think-right-now/1100-6482376/|website=[[GameSpot]]|language=en-US|archive-url=https://web.archive.org/web/20200923035935/https://www.gamespot.com/articles/among-us-is-even-more-popular-than-you-think-right-now/1100-6482376/|archive-date=September 23, 2020|access-date=September 24, 2020|url-status=live}}</ref><ref name=":16" /><ref>{{Cite web|date=2021-12-08|title=Disguised Toast Talks More About Not Being Invited to Jimmy Fallon Among Us Game|url=https://gamerant.com/disguised-toast-jimmy-fallon-not-invited/|website=Game Rant|language=en-US|access-date=2022-01-04}}</ref> |
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The [[COVID-19 pandemic]] was frequently cited as a reason for the popularity of ''Among Us'', as it allowed for socializing despite [[Social distancing measures related to the COVID-19 pandemic|social distancing]].<ref name="improb" /><ref>{{Cite web|title=What is 'Among Us', and How Did It Get So Popular? – Review Geek|url=https://www.reviewgeek.com/58061/what-is-among-us-and-how-did-it-get-so-popular/|website=www.reviewgeek.com|language=en-US|access-date=April 7, 2021}}</ref><ref>{{Cite web|last=Epstein|first=Adam|title=How an obscure 2018 computer game became a global phenomenon overnight|url=https://qz.com/1911718/how-among-us-became-a-global-video-game-phenomenon/|website=[[Quartz (publication)|Quartz]]|language=en|archive-url=https://web.archive.org/web/20201002010031/https://qz.com/1911718/how-among-us-became-a-global-video-game-phenomenon/|archive-date=October 2, 2020|access-date=October 2, 2020|ref=none|url-status=live}}</ref><ref>{{Cite web|last=Stuart|first=Keith|date=September 29, 2020|title=Among Us is the ultimate party game of the Covid era|url=http://www.theguardian.com/games/2020/sep/29/among-us-the-ultimate-party-game-of-the-covid-era|website=[[The Guardian]]|language=en|access-date=October 2, 2020|ref=none}}</ref><ref>{{Cite web|last=Sands|first=Sean|date=August 23, 2020|title='Among Us' Is Not Just the Game of 2020, It's '2020: The Game'|url=https://www.vice.com/en/article/ep43yz/among-us-is-not-just-the-game-of-2020-its-2020-the-game|website=[[Vice Media|Vice]]|language=en|archive-url=https://web.archive.org/web/20201001082837/https://www.vice.com/en/article/ep43yz/among-us-is-not-just-the-game-of-2020-its-2020-the-game|archive-date=October 1, 2020|access-date=October 2, 2020|ref=none|url-status=live}}</ref> Emma Kent of ''[[Eurogamer]]'' believed that the release of Innersloth's ''The Henry Stickmin Collection'' also contributed to awareness of ''Among Us'',<ref name=":15" /> and ''[[PC Gamer]]''<nowiki/>'s Wes Fenlon credited Twitch streamer SR_Kaif for "prim[ing] ''Among Us'' for its big moment." Fenlon also praised ''Among Us'' for improvements over other popular tabletop games that had been inspired by Mafia, such as ''[[Secret Hitler]]''. He said other video game adaptation of Mafia such as ''[[Town of Salem]]'' and ''[[Werewolves Within]]'' were "just add[ing] an online interface for the basic Werewolf rules," whereas ''Among Us'' is as an entirely new take on the concept.<ref name=":16" /> Along with ''[[Fall Guys]]'' and the ''[[Jackbox Party Pack|Jackbox Party Packs]]'', ''Among Us'' provided a narrative-less experience that helped to avoid the "cultural trauma" of the pandemic, according to M.J. Lewis of ''[[Wired (magazine)|Wired]]''.<ref>{{cite magazine|last=Lewis|first=M.J.|date=December 4, 2020|title=Among Us and a Resurgence of Narrative-Free Games|url=https://www.wired.com/story/among-us-narrative-free-games-pandemic-coronavirus/|magazine=[[Wired (magazine)|Wired]]|access-date=December 4, 2020}}</ref> |
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showing the conversion factor from given <math>\log_k</math>-values to their corresponding <math>\log_b </math>-values to be <math>(\log_k b)^{-1}.</math> |
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{{Collapse bottom}}Adapun [[kalkulator ilmiah]] yang menghitung logaritma dengan bilangan pokok 10 dan {{mvar|[[e (mathematical constant)|e]]}}.<ref>{{Citation|last1=Bernstein|first1=Stephen|last2=Bernstein|first2=Ruth|title=Schaum's outline of theory and problems of elements of statistics. I, Descriptive statistics and probability|publisher=[[McGraw-Hill]]|location=New York|series=Schaum's outline series|isbn=978-0-07-005023-5|year=1999|url=https://archive.org/details/schaumsoutlineof00bern}}, hlm. 21</ref> Logaritma terhadap setiap bilangan pokok {{mvar|b}} dapat ditentukan menggunaka menggunakan kedua logaritma tersebut melalui rumus sebelumnya: |
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=== Kumpulan meme dan fitur mod === |
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: <math> ^b\!\log x = \frac{^{10}\!\log x}{^{10}\!\log b} = \frac{^{e}\!\log x}{^{e}\!\log b}.</math> |
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Popularitas ''Among Us'' berlanjut pada beberapa bulan ke depan. [[YouTube]] melaporkan bahwa video tentang ''Among Us'' dilihat sebanyak 4 juta kali pada September 2020,<ref name="youtube">{{citation|title="Among Us" Surged in September – "Among Us" videos topped 4 billion views in September|date=October 14, 2020|url=https://www.youtube.com/trends/articles/among-us-september/|work=[[YouTube|YouTube Culture and Trends]]|archive-url=https://web.archive.org/web/20201015160744/https://www.youtube.com/trends/articles/among-us-september/|quote=Among Us is an online multiplayer social deduction game developed by an American indie game studio, Innersloth. Among Us is a space-themed game in which a crew of astronauts must complete tasks while trying to figure out who among them is an imposter, who is sabotaging their work and killing the other players. The game has been available for about two years, but viewership of videos related to the game soared last month. There were over 4 billion views of videos related to Among Us in September.|access-date=October 14, 2020|archive-date=October 15, 2020|url-status=live}}</ref> dan video [[TikTok]] yang mengandung topik ''Among Us'' dilihat sebanyak lebih dari 13 juta kali pada Oktober 2020.<ref name="newyorktimes">{{citation|last=Lorenz|first=Taylor|title=With Nowhere to Go, Teens Flock to Among Us – YouTubers, influencers and streamers popularized the multiplayer game. Then their fans started playing too.|date=October 14, 2020|url=https://www.nytimes.com/2020/10/14/style/among-us.html|work=[[The New York Times]]|archive-url=https://web.archive.org/web/20201014204604/https://www.nytimes.com/2020/10/14/style/among-us.html|quote=When an indie game company created Among Us in 2018, it was greeted with little fanfare. The multiplayer game remained under the radar as many games do — until the summer of the pandemic. Eager to keep viewers entertained during quarantine, Chance Morris, known online as Sodapoppin, began streaming the game, created by InnerSloth, to his 2.8 million followers on Twitch in July. By mid-September, Among Us caught on like wildfire. Suddenly major YouTube stars, TikTok influencers, and streamers were playing it. PewDiePie, James Charles, and Dr. Lupo have all played the game for millions.|access-date=October 14, 2020|archive-date=October 14, 2020|url-status=live}}</ref> YouTuber CG5 menulis sebuah lagu bernama"Show Yourself", yang diambil dari permainan ''Among Us'' pada September 2020, dan mendapat lebih dari 60 juta kali lihat dalam empat bulan.<ref>{{Cite news|last=Gravelle|first=Cody|date=November 6, 2020|title=Among Us Music Video Goes Viral After Game Dominates Sales and Streaming|url=https://screenrant.com/among-us-show-yourself-music-video/|work=[[ScreenRant]]|access-date=February 7, 2021}}</ref> {{efn|The song’s popularity led to 2 sequels, Lyin’ To Me and Good To Be Alive, released in November 2020 and February 2021, respectively.}} Pada September 2020, jumlah unduhan ''Among Us'' melebihi sebanyak 100 juta<ref name=":16" /> <u>dan jumlah pemain pada saat itu menaik hingga 1,5 juta pemain secara bersamaan</u><ref name=":3" /><ref>* {{Cite magazine|last=Macgregor|first=Jody|date=September 9, 2020|title=Multiplayer space mystery Among Us hits 1.5 million simultaneous players|url=https://www.pcgamer.com/multiplayer-space-mystery-among-us-hits-15-million-simultaneous-players/|url-status=live|magazine=[[PC Gamer]]|language=en-US|archive-url=https://web.archive.org/web/20200921123259/https://www.pcgamer.com/multiplayer-space-mystery-among-us-hits-15-million-simultaneous-players/|archive-date=September 21, 2020|access-date=September 12, 2020|ref=none}} |
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* {{Cite news|last=O'Connor|first=Alice|date=September 8, 2020|title=Among Us had 1.5 million people playing at the same time this weekend|url=https://www.rockpapershotgun.com/2020/09/08/among-us-had-1-5-million-people-playing-at-the-same-time-this-weekend/|language=en-US|archive-url=https://web.archive.org/web/20200909025017/https://www.rockpapershotgun.com/2020/09/08/among-us-had-1-5-million-people-playing-at-the-same-time-this-weekend/|archive-date=September 9, 2020|access-date=September 12, 2020|ref=none|website=[[Rock Paper Shotgun]]|url-status=live}} |
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* {{Cite web|last=Bailey|first=Dustin|date=September 7, 2020|title=Among Us reaches 1.5 million concurrent players|url=https://www.pcgamesn.com/among-us/player-count|website=[[PCGamesN]]|language=en-GB|archive-url=https://web.archive.org/web/20200909025026/https://www.pcgamesn.com/among-us/player-count|archive-date=September 9, 2020|access-date=September 8, 2020|ref=none|url-status=live}} |
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* {{Cite web|last=Zheng|first=Jenny|date=September 18, 2020|title=Among Us Is Really, Really Popular Right Now|url=https://www.gamespot.com/articles/among-us-is-really-really-popular-right-now/1100-6482376/|website=[[GameSpot]]|language=en-US|archive-url=https://web.archive.org/web/20200921123301/https://www.gamespot.com/articles/among-us-is-really-really-popular-right-now/1100-6482376/|archive-date=September 21, 2020|access-date=September 19, 2020|ref=none|url-status=live}}</ref><sup>[terj. kasar]</sup> (nearly 400 thousand of which were on Steam),<ref name=":11" /> then peaked at 3.8 million in late September.<ref>{{Cite web|last=Lugris|first=Mark|date=September 29, 2020|title=Among Us Had 3.8 Million Concurrent Players Last Weekend|url=https://www.thegamer.com/among-us-3-8-million-concurrent-players-last-weekend/|website=TheGamer|language=en-US|archive-url=https://web.archive.org/web/20201001152149/https://www.thegamer.com/among-us-3-8-million-concurrent-players-last-weekend/|archive-date=October 1, 2020|access-date=October 1, 2020|url-status=live}}</ref> The sudden increase in players overloaded the game's server, which according to Willard was "a totally free [[Amazon (company)|Amazon]] server, and it was terrible." This forced him to work quickly, under [[Crunch time (video gaming)|crunch time]], to resolve these issues.<ref name=":14" /> |
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In August, Innersloth opened an online store for ''Among Us'' themed merchandise.<ref name="gamerantsequel" /><ref name=":4" /> The game's popularity inspired many original songs, [[Fan art|fanarts]] and [[Internet meme|internet memes]],<ref name=":20" /><ref name=":0" /><ref name=":14" /> Willard expressed that fan-created content "really is the best part" of making ''Among Us'', and Bromander called it "my favorite thing to see".<ref name=":14" /> The game popularized the slang word "sus" (meaning "suspicious" or "suspect"),<ref name="cnbc">{{citation|last=Rodriguez|first=Salvador|title=How Amazon's Twitch turned an obscure game called Among Us into a pandemic mega-hit|date=October 14, 2020|url=https://www.cnbc.com/2020/10/14/how-among-us-became-a-mega-hit-thanks-to-amazon-twitch.html|work=[[CNBC]]|archive-url=https://web.archive.org/web/20201015160729/https://www.cnbc.com/2020/10/14/how-among-us-became-a-mega-hit-thanks-to-amazon-twitch.html|quote=Developed by InnerSloth, a small studio in Redmond, Washington, Among Us was download nearly 42 million times on Steam in the first half of September, according to Safebettingsites.com, and it was downloaded nearly 84 million times on iOS and Android that month, according to SensorTower. The game hasn’t left the top five on Apple’s U.S. App Store since Sept. 1, and it has seen more than 158 million installs worldwide across the App Store and Google Play to date, SensorTower says.|access-date=October 14, 2020|archive-date=October 15, 2020|url-status=live}}</ref><ref>{{Cite web|last=Marshall|first=Cass|date=September 21, 2020|title=Among Us fans are calling everything 'pretty sus,' and it keeps working|url=https://www.polygon.com/2020/9/21/21449498/among-us-fans-pretty-sus-meme-explained|website=[[Polygon (website)|Polygon]]|language=en|archive-url=https://web.archive.org/web/20200924153115/https://www.polygon.com/2020/9/21/21449498/among-us-fans-pretty-sus-meme-explained|archive-date=September 24, 2020|access-date=October 15, 2020|url-status=live}}</ref><ref>{{Cite web|last=Kim|first=Alina|date=October 5, 2020|title=Red Is Lowkey Sus: A Political Reflection on "Among Us"|url=https://www.chicagomaroon.com/article/2020/10/5/red-lowkey-sus-political-reflection-among-us/|website=[[The Chicago Maroon]]|language=en|archive-url=https://web.archive.org/web/20201015160736/https://www.chicagomaroon.com/article/2020/10/5/red-lowkey-sus-political-reflection-among-us/|archive-date=October 15, 2020|access-date=October 15, 2020|url-status=live}}</ref> which had been used before the game's release.<ref>{{Cite web|title=Sus {{!}} Definition of Sus by Oxford Dictionary on Lexico.com also meaning of Sus|url=https://www.lexico.com/definition/sus|website=Lexico Dictionaries {{!}} English|language=en|access-date=October 19, 2020}}</ref> Other slang terms as well as internet memes popularized and inspired by ''Among Us'' include 'Sussy' and 'Sussy [[Baka (Japanese word)|Baka]]' (derived from "sus"),<ref>{{cite web|date=5 May 2021|title=What is "Sussy Baka" on TikTok? Among Us & anime trend goes viral|url=https://www.dexerto.com/entertainment/what-is-sussy-baka-on-tiktok-among-us-anime-trend-goes-viral-1567557/|website=Dexerto|language=en|access-date=1 April 2022}}</ref><ref>{{cite web|last=Ainswroth|first=Harry|date=5 April 2021|title=What does 'sussy baka' mean and why does everyone on TikTok say it?|url=https://thetab.com/uk/2021/05/04/sussy-baka-203893|website=The Tab|access-date=1 August 2021}}</ref> 'When the Imposter is Sus' (an [[Internet meme|ironic meme]] based on ''Among Us'', usually alongside an edited photo of [[Jerma985]]),<ref>{{Cite web|title=When The Imposter Is Sus/Sus Jerma|url=https://knowyourmeme.com/memes/when-the-imposter-is-sus-sus-jerma|website=Know Your Meme|archive-url=https://web.archive.org/web/20201205012311/https://knowyourmeme.com/memes/when-the-imposter-is-sus-sus-jerma|archive-date=December 5, 2020|url-status=live}}</ref> and 'Amogus' ([[satiric misspelling]] of "''Among Us''").<ref>{{cite web|date=16 September 2021|title=Fellow fans of legumes, take a gander at these official Among Us costumes|url=https://nintendowire.com/news/2021/09/16/fellow-fans-of-legumes-take-a-gander-at-these-official-among-us-costumes/|website=Nintendo Wire|access-date=17 September 2021}}</ref><ref>{{cite web|date=4 March 2021|title=Random: 'Amogus' Is A Playable Among Us Pokémon Hack|url=https://www.nintendolife.com/news/2021/03/random_amogus_is_a_playable_among_us_pokemon_hack|website=Nintendo Life|access-date=17 September 2021}}</ref> |
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Diberikan suatu bilangan {{mvar|x}} dan logaritma {{math|1=''y'' = log<sub>''b''</sub> ''x''}}, dengan {{mvar|b}} adalah bilangan pokok yang tidak diketahui. Bilangan pokok logaritma dapat dirumuskan sebagai |
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During its time of widespread popularity, ''Among Us'' was controversially played by the [[U.S. Navy Esports|U.S. Navy Esports team]], in which players on the stream used in-game names referencing the [[N-word]] and the [[Atomic bombings of Hiroshima and Nagasaki|bombing of Nagasaki]]. The stream was deemed "offensive" and "intolerable" by some viewers.<ref>* {{Cite web|last=Lemon|first=Jacon|date=September 13, 2020|title=US Navy's Twitch account criticized for streaming games with offensive player names|url=https://www.newsweek.com/us-navys-twitch-account-criticized-streaming-games-offensive-player-names-1531578|website=[[Newsweek]]|language=en|archive-url=https://web.archive.org/web/20200921123308/https://www.newsweek.com/us-navys-twitch-account-criticized-streaming-games-offensive-player-names-1531578|archive-date=September 21, 2020|access-date=September 15, 2020|ref=none|url-status=live}} |
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: <math> b = x^\frac{1}{y},</math> |
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* {{Cite web|last=Gault|first=Matthew|date=September 14, 2020|title=A U.S. Navy Twitch Stream Included Jokes About Nagasaki and the N-Word|url=https://www.vice.com/en_us/article/7kp3db/a-us-navy-twitch-stream-included-jokes-about-nagasaki-and-the-n-word|website=[[Vice Media|Vice]]|language=en|archive-url=https://web.archive.org/web/20200921123259/https://www.vice.com/en_us/article/7kp3db/a-us-navy-twitch-stream-included-jokes-about-nagasaki-and-the-n-word|archive-date=September 21, 2020|access-date=September 15, 2020|ref=none|url-status=live}} |
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* {{Cite web|last=Grayson|first=Nathan|date=September 15, 2020|title=Navy Twitch Stream Spirals Out Of Control Due To Slur, War Crime Jokes|url=https://www.kotaku.com.au/2020/09/navy-twitch-stream-spirals-out-of-control-due-to-slur-war-crime-jokes/|website=[[Kotaku Australia]]|language=en-AU|archive-url=https://web.archive.org/web/20200921123338/https://www.kotaku.com.au/2020/09/navy-twitch-stream-spirals-out-of-control-due-to-slur-war-crime-jokes/|archive-date=September 21, 2020|access-date=September 17, 2020|ref=none|url-status=live}} |
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* {{Cite web|last=Marchetto|first=Claudia|date=September 14, 2020|title=Among Us: la Marina americana lo gioca su Twitch usando nickname razzisti ed è bufera|url=https://www.eurogamer.it/articles/2020-09-14-news-videogiochi-among-us-giocato-twitch-marina-militare-usa-nickname-razzisti|website=[[Eurogamer|Eurogamer.it]]|language=it|archive-url=https://web.archive.org/web/20200921123341/https://www.eurogamer.it/articles/2020-09-14-news-videogiochi-among-us-giocato-twitch-marina-militare-usa-nickname-razzisti|archive-date=September 21, 2020|access-date=September 15, 2020|ref=none|url-status=live}}</ref> In October 2020, U.S. Representatives [[Alexandria Ocasio-Cortez]] and [[Ilhan Omar]] streamed the game alongside several other prominent streamers such as [[Pokimane]] and [[Hasan Piker]] as a way to encourage people to vote in the [[2020 United States presidential election]], drawing almost 700,000 concurrent viewers on Twitch.<ref>{{Cite web|last=Brown|first=Abram|date=October 20, 2020|title=Almost 700,000 People Flock To Twitch To Watch Alexandria Ocasio-Cortez Play Hit Video Game 'Among Us'|url=https://www.forbes.com/sites/abrambrown/2020/10/20/almost-700000-people-flock-to-twitch-to-watch-alexandria-ocasio-cortez-play-hit-video-game-among-us/|website=[[Forbes]]|language=en|access-date=October 21, 2020}}</ref><ref>{{cite web|last=Ziady|first=Hanna|date=October 21, 2020|title=Alexandria Ocasio-Cortez just played a video game on Twitch to encourage voting|url=https://www.cnn.com/2020/10/21/tech/aoc-twitch-account-voting/index.html|work=[[CNN]]|access-date=October 21, 2020}}</ref><ref>{{Cite web|title=Alexandria Ocasio-Cortez Streams On Twitch With Hasan Piker And Pokimane, Draws Over 430,000 Viewers|url=https://kotaku.com/alexandria-ocasio-cortez-streams-on-twitch-with-hasan-p-1845431479|website=[[Kotaku]]|language=en-us|access-date=October 21, 2020}}</ref> |
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Permainan video ini juga menerima beberapa mod yang dibuat oleh kounitas, seperti menambahkan peran baru, mode permainan, kosmetik, dsb.<ref>{{Cite magazine|last=Matheus|first=Emma|date=March 22, 2021|title=The best Among Us mods to try with your friends|url=https://www.pcgamer.com/best-among-us-mod-download/|magazine=[[PC Gamer]]|access-date=March 25, 2021}}</ref> ''Among Us'' juga ditampilkan di [[Twitch Rivals|Twitch Rivals 2020]], sebuah turnamen permainan daring yang diselenggarakan pada 4 Desember 2020.<ref>{{Cite web|last=Mukherjee|first=Arnab|date=December 6, 2020|title=Twitch Rivals Among Us Showdown: Trainwrecks wins for the 4th time in a row, Glitch Pet Twitch Drops active on his channel!|url=https://thesportsrush.com/among-us-news-twitch-rivals-among-us-showdown-trainwrecks-wins-for-the-4th-time-in-a-row-glitch-pet-twitch-drops-active-on-his-channel/|website=The Sports Rush|access-date=March 25, 2021}}</ref> Selama perayaan tersebut, pemain dapat menerima sebuah ''exclusive pet'' yang disebut "Glitch Pet", yang berupakan logo Twitch.<ref>{{Cite web|last=Sayles|first=Lauren|date=December 9, 2020|title=How to get the free Twitch Glitch pet to use in Among Us|url=https://www.pcinvasion.com/twitch-glitch-pet-among-us/|website=PC Invasion|access-date=March 25, 2021}}</ref> |
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Rumus tersebut dapat diperlihatkan dengan mengambil persamaan yang mendefinisikan <math> x = b^{\,\log_b x} = b^y</math>, lalu dipangkatkan dengan <math>\tfrac{1}{y}.</math> |
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== |
=== Manga === |
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Pada 28 Desember 2021, H2 Interactive, yang menerbitkan ''Among Us'' di Jepang, mengumumkan bahwa [[manga]] [[One-shot (komik)|one-shot]] yang diambil dari permainan tersebut akan dipublikasikan dalam masalah April ''[[CoroCoro Comic|Bessatsu CoroCoro]]'' pada ''28'' Februari 2022.<ref>{{cite web|last=Morrissy|first=Kim|date=January 14, 2022|title=Among Us Video Game Gets 1-Shot Manga In February|url=https://www.animenewsnetwork.com/interest/2022-01-13/among-us-video-game-gets-1-shot-manga-in-february/.181454|publisher=[[Anime News Network]]|access-date=January 15, 2022}}</ref><ref>{{cite tweet|author=H2 INTERACTIVE公式アカウント|user=H2InteractiveJP|number=1475738512381321220|title=Among Usの読み切り漫画が別冊コロコロ4月号に登場します!お楽しみに⭐️|access-date=January 15, 2022|language=ja}}</ref> Pada 13 Januari, Innersloth mulai mempromosikan manganya melalui akun [[Twitter]] resminya.<ref>{{cite tweet|author=Innersloth|user=InnerslothDevs|number=1481356564673880067|title=Surpriseeeee! @AmongUsGame will have a 1 shot manga feature in Bessatsu Corocoro magazine on April 2022 Sparkles|access-date=January 15, 2022|language=ja}}</ref> |
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[[Berkas:Log4.svg|jmpl|Grafik logaritma dengan bilangan pokok 0,5; 2; dan {{mvar|e}}]] |
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Terdapat tiga bilangan pokok yang umum, di antara semua pilihan bilangan pokok pada logaritma. Ketiga bilangan pokok tersebut adalah {{math|1=''b'' = 10}}, {{math|1=''b'' = [[e (mathematical constant)|''e'']]}} (konstanta [[bilangan irasional]] yang kira-kira sama dengan 2.71828), dan {{math|1=''b'' = 2}} ([[logaritma biner]]). Dalam [[analisis matematika]], logaritma dengan bilangan pokok {{mvar|e}} tersebar karena sifat analitik yang dijelaskan di bawah. Di sisi lain, logaritma dengan {{nowrap|bilangan pokok 10}} mudah dipakai dalam perhitungan manual dalam sistem bilangan [[desimal]]:<ref>{{Citation|last1=Downing|first1=Douglas|title=Algebra the Easy Way|series=Barron's Educational Series|location=Hauppauge, NY|publisher=Barron's|isbn=978-0-7641-1972-9|date=2003|url=https://archive.org/details/algebraeasyway00down_0}}, chapter 17, p. 275</ref> |
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== Sambutan ==<!-- Do not switch "imposter" to "impostor" in the Evelyn Lau quote. Do not add "sic" either, as "imposter" is a correct spelling. --> |
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: <math>^{10}\!\log(10 x) = \, ^{10}\!\log 10 + \, ^{10}\!\log x = 1 + \, ^{10}\!\log x.\ </math> |
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{{Video game reviews|qid=none|MC=PC: 85/100<ref name="MCPC">{{cite Metacritic |id=among-us |type=game |vgtype=pc |title=Among Us (PC) |access-date=February 14, 2021}}</ref><br />[[Nintendo Switch|Switch]]: 79/100<ref name="MCSwitch">{{cite Metacritic |id=among-us |type=game |vgtype=switch|title=Among Us (Switch) |access-date=February 14, 2021}}</ref>|4P=68/100<ref>{{Cite web|url=https://www.4players.de/4players.php/dispbericht/Switch/Test/42379/84750/0/Among_Us.html|title=Test: Among Us|last=Krosta|first=Michael|date=February 3, 2021|website=[[4Players]]|access-date=April 11, 2021}}</ref>|GI=8/10<ref>{{Cite magazine|url=https://www.gameinformer.com/review/among-us/among-us-review-better-late-than-never|title=Among Us Review – Better Late Than Never|last=Ruppert|first=Liana|date=September 29, 2020|magazine=Game Informer|access-date=October 29, 2020|url-status=live|archive-url=https://web.archive.org/web/20201115112314/https://www.gameinformer.com/review/among-us/among-us-review-better-late-than-never|archive-date=November 15, 2020}}</ref>|JXV=14/20<ref name="JXV">{{Cite web|url=https://www.jeuxvideo.com/test/1327943/among-us-que-vaut-vraiment-le-party-game-du-confinement.htm|title=Test : Among Us : Que vaut vraiment le party game du confinement ?|author=Tiraxa|date=November 23, 2020|website=Jeuxvideo.com|access-date=November 28, 2020|url-status=live|archive-url=https://web.archive.org/web/20201127052408/https://www.jeuxvideo.com/test/1327943/among-us-que-vaut-vraiment-le-party-game-du-confinement.htm|archive-date=November 27, 2020}}</ref>|IGN=9/10<ref name="IGNReview" />|NLife=8/10<ref name="NintendoLife">{{Cite web|first1 = PJ|last1 = O'Reilly|url = https://www.nintendolife.com/reviews/switch-eshop/among_us|title = Among Us Review (Switch eShop)|website = Nintendo Life|date = December 21, 2020|access-date = February 7, 2021|language = en-US}}</ref>|PCM=4/5 (iOS)<ref name="PCMag">{{cite web |url= https://www.pcmag.com/reviews/among-us-for-ios |title= Among Us (for iOS) Review |last= Minor |first= Jordan |date= 28 October 2020 |website= PCMag |access-date= 23 January 2022}}</ref>|PSQ=7/10<ref name="Push Square">{{cite web |url= https://www.pushsquare.com/reviews/ps5/among-us |title= Mini Review: Among Us (PS5) - Social Deduction Sensation Is Best with Buddies |last= Barker |first= Sammy |date= 24 December 2021 |website= Push Square |access-date= 23 January 2022}}</ref>}} |
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''Among Us'' was well received by critics. On the aggregator website [[Metacritic]], the PC port received a 85 of 100 score based on 9 critic reviews, while the [[Nintendo Switch]] version received a 79 of 100 score based on 9 critic reviews, both them indicating "generally favorable reviews".<ref name="MCPC" /><ref name="MCSwitch" /> It was also considered one of the "Best PC Games for 2018", being ranked 17th, and as the "#38 Best Discussed PC Game of 2018".<ref>{{Cite web|title=Best PC Games for 2018|url=https://www.metacritic.com/browse/games/score/metascore/year/pc/filtered?sort=desc&year_selected=2018|website=[[Metacritic]]|access-date=March 25, 2021}}</ref><ref>{{Cite web|title=Best PC Video Games|url=https://www.metacritic.com/browse/games/score/metascore/discussed/pc/filtered?sort=desc&year_selected=2018|website=[[Metacritic]]|access-date=March 25, 2021}}</ref> Since December 2020, ''[[IGN]]'' considered it one of 2020's best reviewed games so far.<ref>{{Cite web|last=Sirani|first=Jordan|date=September 25, 2020|title=The Best Reviewed Games of 2020|url=https://www.ign.com/articles/the-best-reviewed-games-of-2020-so-far|website=[[IGN]]|access-date=March 30, 2021}}</ref> |
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Jadi, {{math|log<sub>10</sub> ''x''}} berkaitan dengan jumlah [[digit desimal]] suatu bilangan bulat positif {{mvar|x}}: jumlah digitnya merupakan [[bilangan bulat]] terkecil yang lebih besar dari {{math|<sup>10</sup>log ''x''}}.<ref>{{Citation|last1=Wegener|first1=Ingo|title=Complexity theory: exploring the limits of efficient algorithms|publisher=[[Springer-Verlag]]|location=Berlin, New York|isbn=978-3-540-21045-0|date=2005}}, p. 20</ref> Sebagai contoh, {{math|<sup>10</sup>log 1430}} kira-kira sama dengan 3,15. Bilangan berikutnya merupakan jumlah digit dari 1430, yaitu 4. Dalam [[teori informasi]], logaritma alami dipakai dalam [[Nat (unit)|nat]] dan logaritma dengan bilangan pokok 2 dipakai dalam [[bit]] sebagai satuan dasar informasi.<ref>{{citation|title=Information Theory|first=Jan C. A.|last=Van der Lubbe|publisher=Cambridge University Press|date=1997|isbn=978-0-521-46760-5|page=3|url={{google books |plainurl=y |id=tBuI_6MQTcwC|page=3}}}}</ref> Logaritma biner juga dipakai dalam [[sistem biner]] ada yang dimana-mana dalam [[ilmu komputer]]. Dalam [[teori musik]], rasio tinggi nada kedua (yaitu [[oktaf]]) ada di mana-mana dan jumlah [[Sen (musik)|sen]] antara setiap dua tinggi nada dirumuskan sebagai konstanta 1200 dikali logaritma dari rasio (yaitu, 100 sen per [[setengah nada]] dengan [[temperamen yang sama]]). Dalam [[fotografi]], logaritma dengan bilangan pokok dua dipakai untuk mengukur [[nilai eksposur]], [[Luminans|tingkatan cahaya]], [[waktu eksposur]], [[tingkap]], dan [[kecepatan film]] dalam "stop".<ref>{{citation|title=The Manual of Photography|first1=Elizabeth|last1=Allen|first2=Sophie|last2=Triantaphillidou|publisher=Taylor & Francis|date=2011|isbn=978-0-240-52037-7|page=228|url={{google books |plainurl=y |id=IfWivY3mIgAC|page=228}}}}</ref> |
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Elliott Osange of ''Bonus Stage'' considered that the game is "silly fun", but felt that is more fun "to be an Impostor".<ref name=":27">{{Cite web|last=Osange|first=Elliott|date=September 23, 2020|title=Among Us Review|url=https://www.bonusstage.co.uk/2020/09/23/among-us-review/|website=Bonus Stage|access-date=March 15, 2021}}</ref> Craig Pearson of ''[[Rock, Paper, Shotgun]]'' had the same opinion, found playing as an Impostor "a lot more fun" than playing as a Crewmate, which he called "exhausting".<ref name=":1" /> In reference to the game's popularity among streamers, Evelyn Lau of ''[[The National (Abu Dhabi)|The National]]'' said: "Watching the reactions of people trying to guess who the impostor is (and sometimes getting it very wrong) or lying terribly about not being the impostor is all quite entertaining."<ref name=":2" /> Alice O'Conner of ''Rock, Paper, Shotgun'' described the game as "Mafia or Werewolf but with minigames".<ref>{{Cite news|author=O'Conner|first=Alice|date=September 8, 2020|title=Among Us had 1.5 million people playing at the same time this weekend|url=https://www.rockpapershotgun.com/2020/09/08/among-us-had-1-5-million-people-playing-at-the-same-time-this-weekend/|archive-url=https://web.archive.org/web/20200909025017/https://www.rockpapershotgun.com/2020/09/08/among-us-had-1-5-million-people-playing-at-the-same-time-this-weekend/|archive-date=September 9, 2020|access-date=September 8, 2020|url-status=live|website=[[Rock Paper Shotgun]]}}</ref> Andrew Penney of ''TheGamer'' said the game was "worth it for the price" and that "who you play with dictates how fun the game is."<ref name=":5" /> L'avis de Tiraxa of ''[[Jeuxvideo.com]]'' praised the game's Freeplay mode, which offers newer players "to browse the map alone to accommodate the places", as they would need to play several games in order to "perfect their strategies".<ref name="JXV" /> |
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Tabel berikut memuat notasi-notasi umum mengenai bilangan pokok beserta bidang yang dipakai. Ada beberapa mata pelajaran yang menulis {{math|log ''x''}} daripada {{math|log<sub>''b''</sub> ''x''}}, dan adapula notasi {{math|<sup>''b''</sup>log ''x''}} yang juga muncul pada beberapa mata pelajaran.<ref>{{Citation|url=http://www.mathe-online.at/mathint/lexikon/l.html|author1=Franz Embacher|author2=Petra Oberhuemer|title=Mathematisches Lexikon|publisher=mathe online: für Schule, Fachhochschule, Universität unde Selbststudium|access-date=22 March 2011|language=de}}</ref> Pada kolom "Notasi ISO" memuat penamaan yang disarankan berdasarkan [[International Organization for Standardization]] ([[ISO 80000-2]]).<ref>Quantities and units – Part 2: Mathematics (ISO 80000-2:2019); EN ISO 80000-2</ref> Karena notasi {{math|log {{mvar|x}}}} telah dipakai untuk ketiga bilangan pokok di atas (atau ketika bilangan pokok belum ditentukan), bilangan pokok yang dimaksud harus sering diduga tergantung konteks atau mata pelajarannya. Sebagai contoh, {{Math|log}} biasanya mengacu pada {{math|<sup>2</sup>log}} dalam ilmu komputer, dan {{Math|log}} mengacu pada {{math|<sup>''e''</sup>log}}.<ref>{{citation|first1=Michael T.|last1=Goodrich|author1-link=Michael T. Goodrich|first2=Roberto|last2=Tamassia|author2-link=Roberto Tamassia|title=Algorithm Design: Foundations, Analysis, and Internet Examples|publisher=John Wiley & Sons|date=2002|page=23|quote=One of the interesting and sometimes even surprising aspects of the analysis of data structures and algorithms is the ubiquitous presence of logarithms ... As is the custom in the computing literature, we omit writing the base {{mvar|b}} of the logarithm when {{math|1=''b'' = 2}}.}}</ref> Dalam konteks lainnya, {{Math|log}} seringkali mengacu pada {{math|log<sub>10</sub>}}.<ref>{{citation|title=Introduction to Applied Mathematics for Environmental Science|edition=illustrated|first1=David F.|last1=Parkhurst|publisher=Springer Science & Business Media|date=2007|isbn=978-0-387-34228-3|page=288|url={{google books |plainurl=y |id=h6yq_lOr8Z4C|page=288 }}}}</ref> |
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{| class="wikitable" style="text-align:center; margin:1em auto 1em auto;" |
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! scope="col" |Bilangan pokok |
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{{mvar|b}} |
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! scope="col" |Nama {{Math|<sup>''b''</sup>log ''x''}} |
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! scope="col" |Notasi ISO |
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! scope="col" |Notasi lain |
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! scope="col" |Dipakai dalam bidang |
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|- |
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! scope="row" |2 |
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|[[logaritma biner]] |
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|{{math|lb ''x''}}<ref name="gullberg">{{Citation|title=Mathematics: from the birth of numbers.|author=Gullberg, Jan|location=New York|publisher=W. W. Norton & Co|date=1997|isbn=978-0-393-04002-9|url-access=registration|url=https://archive.org/details/mathematicsfromb1997gull}}</ref> |
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|{{math|ld ''x''}}, {{math|log ''x''}}, {{math|lg ''x''}},<ref>See footnote 1 in {{citation|last1=Perl|first1=Yehoshua|last2=Reingold|first2=Edward M.|title=Understanding the complexity of interpolation search|journal=Information Processing Letters|date=December 1977|volume=6|issue=6|pages=219–22|doi=10.1016/0020-0190(77)90072-2}}</ref> {{math|<sup>2</sup>log ''x''}} |
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|[[ilmu komputer]], [[teori informasi]], [[bioinformatika]], [[teori musik]], [[fotografi]] |
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|- |
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! scope="row" |{{mvar|e}} |
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|[[logaritma alami]] |
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|{{math|ln ''x''}}{{refn|Some mathematicians disapprove of this notation. In his 1985 autobiography, [[Paul Halmos]] criticized what he considered the "childish ln notation," which he said no mathematician had ever used.<ref> |
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{{Citation |
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|title = I Want to Be a Mathematician: An Automathography |
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|author = Paul Halmos |
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|publisher = Springer-Verlag |
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|location=Berlin, New York |
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|date = 1985 |
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|isbn=978-0-387-96078-4 |
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}}</ref> |
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The notation was invented by [[Irving Stringham]], a mathematician.<ref> |
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{{Citation |
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|title = Uniplanar algebra: being part I of a propædeutic to the higher mathematical analysis |
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|author = Irving Stringham |
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|publisher = The Berkeley Press |
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|date = 1893 |
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|page = xiii |
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|url = {{google books |plainurl=y |id=hPEKAQAAIAAJ|page=13}} |
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}}</ref><ref> |
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{{Citation|title = Introduction to Financial Technology|author = Roy S. Freedman|publisher = Academic Press|location=Amsterdam|date = 2006|isbn=978-0-12-370478-8|page = 59|url = {{google books |plainurl=y |id=APJ7QeR_XPkC|page=5}}}}</ref>|name=adaa|group=nb}} |
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|{{math|log {{mvar|x}}}} (dipakai dalam matematika<ref>See Theorem 3.29 in {{citation|last1=Rudin|first1=Walter|title=Principles of mathematical analysis|date=1984|publisher=McGraw-Hill International|location=Auckland|isbn=978-0-07-085613-4|edition=3rd ed., International student|url=https://archive.org/details/principlesofmath00rudi}}</ref> dan beberapa [[bahasa pemrograman]] lainnya{{refn|For example [[C (programming language)|C]], [[Java (programming language)|Java]], [[Haskell (programming language)|Haskell]], and [[BASIC programming language|BASIC]].|group=nb}}), {{math|<sup>''e''</sup>log ''x''}} |
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|matematika, fisika, kimia, |
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[[statistik]], [[ekonomi]], teori informasi, dan rekayasa |
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|- |
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! scope="row" |10 |
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|[[logaritma biasa]] |
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|{{math|lg ''x''}} |
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|{{math|log ''x''}}, {{math|log<sub>10</sub> ''x''}} |
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(dipakai dalam rekayasa, biologi, dan astronomi) |
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|bidang berbagai [[rekayasa]] (lihat [[decibel|desibel]] dan lihat di bawah), |
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[[tabel]] logaritma, [[kalkulator]] genggam, [[spektroskop]] |
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|- |
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! scope="row" |{{mvar|b}} |
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|logaritma dengan bilangan pokok {{mvar|b}} |
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|{{math|<sup>''b''</sup>log ''x''}} |
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| |
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|matematika |
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|} |
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== Sejarah == |
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{{Main|Sejarah logaritma}} |
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Leana Hafer from ''[[IGN]]'' stated in her verdict on the game: "I don't have any sus that this will be the last game of its breed to make a splash, since we’re already seeing its influence on even mega-games like Fortnite". As a negative point, she pointed out some technical problems, such as the difficulty of finding rooms that aren't already full or are a long way from getting there. She also lamented the lack of "mechanic to punish players who rage-quit when they don't get to play as impostor, or are caught dead to rights in the middle of a murder".<ref name="IGNReview">{{Cite web|last=Hafer|first=Leana|date=December 22, 2020|title=Among Us Review|url=https://www.ign.com/articles/among-us-review|website=[[IGN]]}}</ref> Tiraxa of ''[[Jeuxvideo.com]]'' was more critical of the game, lamenting the lack of an inbuilt voice chat, server bugs which "[prevent] some from joining the party, in a totally unexplained way", public servers with strangers, which she considered "less entertaining" than private servers with friends, and the large development progress, stating that the game has a "bit of a way to go before it reaches its full potential".<ref name="JXV" /> The mobile version of the game, although being free-to-play, was criticized. Osange of ''Bonus Stage'' called the presence of ads and in-app purchases of cosmetic changes that are mostly available for free on the PC version "nonsense". He also called the PC version "stable" but also stated that the Android version is "a device-by-device situation".<ref name=":27" /> |
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''Sejarah logaritma'' yang dimulai dari Eropa pada abad ketujuh belas merupakan penemuan [[fungsi (matematika)|fungsi]] baru yang memperluas ranah analisis di luar jangkauan metode aljabar. Metode logaritma dikemukakan secara terbuka oleh [[John Napier]] pada tahun 1614, dalam sebuah buku berjudul ''Mirifici Logarithmorum Canonis Descriptio''.<ref>{{citation|first=John|last=Napier|author-link=John Napier|title=Mirifici Logarithmorum Canonis Descriptio|trans-title=The Description of the Wonderful Rule of Logarithms|language=la|location=Edinburgh, Scotland|publisher=Andrew Hart|year=1614|url=http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN527914568&DMDID=DMDLOG_0001&LOGID=LOG_0001&PHYSID=PHYS_0001}}</ref><ref>{{Citation|first=Ernest William|last=Hobson|title=John Napier and the invention of logarithms, 1614|year=1914|publisher=The University Press|location=Cambridge|url=https://archive.org/details/johnnapierinvent00hobsiala}}</ref> Sebelum penemuan Napier, ada teknik lain dengan jangkauan metode yang serupa, seperti [[prosthafaeresis]] atau penggunaan tabel barisan, yang dikembangkan dengan luas oleh [[Jost Bürgi]] sekitar tahun 1600.<ref name="folkerts">{{citation|last1=Folkerts|first1=Menso|last2=Launert|first2=Dieter|last3=Thom|first3=Andreas|arxiv=1510.03180|doi=10.1016/j.hm.2016.03.001|issue=2|journal=[[Historia Mathematica]]|mr=3489006|pages=133–147|title=Jost Bürgi's method for calculating sines|volume=43|year=2016|s2cid=119326088}}</ref><ref>{{mactutor|id=Burgi|title=Jost Bürgi (1552 – 1632)}}</ref> Napier menciptakan istilah untuk logaritma dalam bahasa Latin Tengah, “logaritmus” yang berasal dari bahasa Yunani, secara harfiah berarti, “rasio-bilangan,” dari ''logos'' “proporsi, rasio, kata” + ''arithmos'' “bilangan”. |
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The Nintendo Switch version received some criticism. William Antonelli of ''[[Insider Inc.|Insider]]'' said that the Switch controls give "many tasks a satisfying game response". However, he also stated that most of the tasks could be "done quickly with the Switch's touchscreen control", which can only be used when the console is in handheld mode. He noted that many of the game's tasks are difficult to complete using a gamepad, which is required when the console is connected to a larger screen, and considered this version "inferior" to the PC and mobile versions.<ref name=":34">{{Cite web|last=Antonelli|first=William|date=December 23, 2020|title='Among Us' is the biggest game of 2020, but don't play it on the Nintendo Switch|url=https://www.insider.com/among-us-nintendo-switch-game-review-2020-12|website=Insider|access-date=February 17, 2021}}</ref> He also stated that the communication system is "frustrating", as using the joystick to select letters is "slow", and said the fact that the game has support for multiplayer across multiple platforms gives Switch players "immediate disadvantage".<ref name=":34" /> PJ O'Reilly of ''Nintendo Life'' noted that the Switch lacked much of the additional content available on other platforms, such as skins, which he called a "shame".<ref name="NintendoLife" /> |
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[[Logaritma biasa]] suatu bilangan adalah indeks pangkat sepuluh yang sama dengan bilangan tersebut.<ref>William Gardner (1742) ''Tables of Logarithms''</ref> Berbicara tentang angka yang membutuhkan banyak angka adalah kiasan kasar untuk logaritma umum, dan disebut oleh [[Archimedes]] sebagai “urutan bilangan”.<ref>{{citation|last=Pierce|first=R. C. Jr.|date=January 1977|doi=10.2307/3026878|issue=1|journal=[[The Two-Year College Mathematics Journal]]|jstor=3026878|pages=22–26|title=A brief history of logarithms|volume=8}}</ref> Logaritma real pertama adalah metode heuristik yang mengubah perkalian menjadi penjumlahan, sehingga memudahkan perhitungan yang cepat. Beberapa metode ini menggunakan tabel yang diturunkan dari identitas trigonometri.<ref>Enrique Gonzales-Velasco (2011) ''Journey through Mathematics – Creative Episodes in its History'', §2.4 Hyperbolic logarithms, p. 117, Springer {{isbn|978-0-387-92153-2}}</ref> Metode tersebut disebut [[prosthafaeresis]]. |
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''Among Us'' has been frequently compared to ''Fall Guys'', as both became popular as party games during the COVID-19 pandemic;<ref name="improb" /><ref name=":10" /><ref name=":18" /> the developers of both games have positively acknowledged each other on [[Twitter]].<ref>{{Cite tweet|number=1308574859144945667|user=FallGuysGame|title=This is actually true<br />We love Among Us 😍|author=[[Fall Guys]]}}</ref><ref>{{Cite tweet|number=1308884508897423363|user=forte_bass|title=This is horrifying.<br />I love it.|author=Forest Willard}}</ref> Comparisons have also been drawn between the two games' [[Avatar (computing)|avatars]], which have been said to look like [[Jelly bean|jelly beans]].<ref>{{Cite web|last=Fairfax|first=Zackerie|date=September 27, 2020|title=A Fall Guys X Among Us Crossover Could Happen (& It Just Makes Sense)|url=https://screenrant.com/fall-guys-among-us-crossover-costume-skin/|website=[[Screen Rant]]|language=en-US|archive-url=https://web.archive.org/web/20201008063055/https://screenrant.com/fall-guys-among-us-crossover-costume-skin/|archive-date=October 8, 2020|access-date=October 4, 2020|url-status=live}}</ref><ref>{{Cite web|last=Harris|first=Iain|date=October 1, 2020|title=Someone has modded Among Us's Red into Left 4 Dead 2, naturally|url=https://www.pcgamesn.com/left-4-dead-2/mod-among-us-red|website=[[PCGamesN]]|language=en-GB|archive-url=https://web.archive.org/web/20201003173555/https://www.pcgamesn.com/left-4-dead-2/mod-among-us-red|archive-date=October 3, 2020|access-date=October 4, 2020|url-status=live}}</ref> ''Among Us'' has also been compared to [[The Thing (1982 film)|''The Thing'']],<ref name=":0" /><ref name=":17" /> ''[[Town of Salem]]'',<ref name=":16" /><ref name=":17" /> ''Werewolves Within'',<ref name=":16" /> and ''[[Secret Hitler]]''.<ref name=":16" /> |
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Penemuan [[fungsi (matematika)|fungsi]] sekarang dikenal sebagai [[logaritma alami]] dimulai sebagai upaya untuk [[kuadratur (matematika)|kuadratur]] dari [[hiperbola]] persegi panjang oleh [[Grégoire de Saint-Vincent]], seorang Yesuit Belgia yang tinggal di Praha. Archimedes telah menulis ''[[The Quadrature of the Parabola]]'' pada abad ketiga SM, tetapi kuadratur untuk hiperbola menghindari semua upaya sampai Saint-Vincent menerbitkan hasilnya pada tahun 1647. Relasi yang disediakan logaritma antara [[barisan dan deret geometri]] dalam [[argumen dari sebuah fungsi|argumen]] dan nilai [[barisan dan deret aritmetika]], [[A. A. de Sarasa]] diminta untuk membuat hubungan kuadratur Saint-Vincent dan tradisi logaritma dalam [[prosthafaeresis]], mengarah ke istilah "logaritma hiperbolik", sebuah persamaan kata untuk logaritma alami. Dengan segera, fungsi baru tersebut dihargai oleh [[Christiaan Huygens]] dan [[James Gregory (matematikawan)|James Gregory]]. Notasi Log y diadopsi oleh [[Gottfried Wilhelm Leibniz|Leibniz]] pada tahun 1675,<ref>[[Florian Cajori]] (1913) "History of the exponential and logarithm concepts", [[American Mathematical Monthly]] 20: 5, 35, 75, 107, 148, 173, 205.</ref> dan tahun berikutnya dia mengaitkannya dengan [[kalkulus integral|integral]] <math display="inline">\int \frac{dy}{y} .</math> |
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=== Sales === |
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Sebelum Euler mengembangkan konsep modernnya tentang logaritma alami kompleks, [[Roger Cotes#Matematika|Roger Cotes]] memiliki hasil yang hampir sama ketika ia menunjukkan pada tahun 1714 bahwa<ref>{{citation|last1=Stillwell|first1=J.|title=Mathematics and Its History|date=2010|publisher=Springer|edition=3rd}}</ref> |
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{{As of|2020|9}}, <u>[[Steam Spy]] estimated that the game had more than {{nowrap|10 million}} owners on [[Steam (service)|Steam]]</u>.<ref>{{cite news|last1=Peters|first1=Jay|date=September 23, 2020|title=Among Us is so popular that its developers just canceled the sequel|url=https://www.theverge.com/2020/9/23/21453499/among-us-2-sequel-popular-canceled-developers-innersloth|work=[[The Verge]]|access-date=February 20, 2021}}</ref> The [[Associated Press]] noted the game was the most downloaded app on the [[App Store (iOS)|iOS App Store]] for both [[IPhone|iPhones]] and [[IPad|iPads]] in October 2020.<ref>{{citation|url=https://www.washingtonpost.com/business/technology/the-top-iphone-and-ipad-apps-on-apple-app-store/2020/10/13/69318488-0d7c-11eb-b404-8d1e675ec701_story.html|title=The top iPhone and iPad apps on Apple App Store|agency=[[Associated Press]]|newspaper=[[The Washington Post]]|date=October 13, 2020|access-date=October 13, 2020|quote=1. Among Us!, InnerSloth LLC|archive-date=October 15, 2020|archive-url=https://web.archive.org/web/20201015160813/https://www.washingtonpost.com/business/technology/the-top-iphone-and-ipad-apps-on-apple-app-store/2020/10/13/69318488-0d7c-11eb-b404-8d1e675ec701_story.html|url-status=dead}}</ref> According to [[SuperData Research]], the game had roughly {{nowrap|500 million}} players worldwide {{as of|2020|11|lc=y}}, with the [[free-to-play]] mobile version accounting for 97% of players and the [[buy-to-play]] PC version accounting for 3% of players, though it was the buy-to-play PC version that generated 64% of the game's gross revenue.<ref>{{cite news|date=December 18, 2020|title=November 2020 worldwide digital games market|url=https://www.superdataresearch.com/blog/worldwide-digital-games-market|work=[[SuperData Research]]|publisher=[[Nielsen Company]]|archive-url=https://web.archive.org/web/20201218193653/http://www.superdataresearch.com/blog/worldwide-digital-games-market|archive-date=December 18, 2020|access-date=December 19, 2020|url-status=dead}}</ref> ''Among Us'' became one of the best selling games of 2020 on Steam, being listed on the platinum category on "The Year's Top 100" list.<ref>{{Cite web|last=Blake|first=Vikki|date=December 28, 2020|title=Steam reveals 2020's most-played and best-selling PC games|url=https://www.gamesradar.com/steam-reveals-2020s-most-played-and-best-selling-pc-games/|website=GamesRadar+|access-date=January 1, 2021}}</ref><ref>{{Cite web|last=Vincent|first=Brittany|date=December 26, 2020|title=Cyberpunk 2077, Among Us Top Steam's Best-Selling Games of 2020|url=https://uk.pcmag.com/pc-games/130697/cyberpunk-2077-among-us-top-steams-best-selling-games-of-2020|website=PCMag|access-date=January 1, 2021}}</ref> The [[Nintendo Switch]] version's launch sold {{nowrap|3.2 million}} digital units in December 2020, making it the highest-earning version of the game for the month and one of the [[List of best-selling Nintendo Switch video games|best-selling games on the Nintendo Switch]].<ref>{{cite news|date=January 22, 2021|title=Worldwide digital games market: December 2020|url=https://www.superdataresearch.com/blog/worldwide-digital-games-market|work=[[SuperData Research]]|publisher=[[Nielsen Company]]|archive-url=https://web.archive.org/web/20210122193846/http://www.superdataresearch.com/blog/worldwide-digital-games-market/|archive-date=January 22, 2021|access-date=January 22, 2021|url-status=live}}</ref><ref>{{Cite web|last=Pastro|first=Max|date=January 25, 2021|title=Among Us Nintendo Switch Version Sold Over 3 Million Units|url=https://screenrant.com/among-us-nintendo-switch-version-sales-december-2020/|website=Screen Rant|access-date=March 15, 2021}}</ref> |
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:<math>\log(\cos \theta + i\sin \theta) = i\theta</math>. |
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Pada Mei 2021, ''Among Us'' ditawarkan sebagai permainan gratis di [[Epic Games Store]] selama seminggu. Rata-rata pemain setiap hari melonjak dari sekitar 350.000 pemain dalam beberapa minggu sebelum mencapai lebih dari 2 juta pemain selama berlangsungnya ''giveaway''.<ref>{{cite web|last=Bailey|first=Dustin|date=May 31, 2021|title=Among Us goes from 350k daily PC players to two million after Epic giveaway|url=https://www.pcgamesn.com/among-us/epic-players|work=[[PCGamesN]]|access-date=May 31, 2021}}</ref> Pada 29 Juni 2021, Innersloth melaporkan di [[Twitter]] bahwa setidaknya ada 15 juta salinan yang diklaim saat mempromisikan permainan gratis di Epic Games Store.<ref>{{Cite web|date=2021-07-01|title=Among Us Downloaded on Epic Games Store 15 Million Times During Giveaway|url=https://screenrant.com/among-us-epic-games-store-15-million-downloads/|website=ScreenRant|language=en-US|access-date=2021-07-01}}</ref> |
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== Tabel logaritma, kaidah geser, dan penerapan bersejarah == |
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[[Berkas:Logarithms_Britannica_1797.png|ka|jmpl|360x360px|Penjelasan logaritma di ''[[Encyclopædia Britannica]]'' pada tahun 1797.]] |
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Dengan menyederhanakan perhitungan yang rumit sebelum adanya mesin hitung komputer, logaritma berkontribusi pada kemajuan pengetahuan, khususnya [[astronomi]]. Logaritma sangat penting terhadap kemajuan dalam [[survei]], [[navigasi benda langit]], dan cabang lainnya. [[Pierre-Simon Laplace]] menyebut logaritma sebagai |
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=== Penghargaan === |
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:: "...[sebuah] kecerdasan mengagumkan, yang mengurangi pekerjaan berbulan-bulan menjadi beberapa hari, menggandakan kehidupan astronom, dan menghindarinya dari kesalahan dan rasa jijik yang tak terpisahkan dari perhitungan yang panjang."<ref>{{Citation|last1=Bryant|first1=Walter W.|title=A History of Astronomy|url=https://archive.org/stream/ahistoryastrono01bryagoog#page/n72/mode/2up|publisher=Methuen & Co|location=London|year=1907}}, p. 44</ref> |
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{| class="wikitable plainrowheaders sortable" width="auto" |
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! scope="col" |Penghargaan |
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Karena fungsi {{math|''f''(''x'') {{=}} {{mvar|b}}<sup>''x''</sup>}} merupakan fungsi invers dari {{math|<sup>''b''</sup>log ''x''}}, fungsi tersebut disebut sebagai '''antilogaritma'''.<ref>{{Citation|editor1-last=Abramowitz|editor1-first=Milton|editor1-link=Milton Abramowitz|editor2-last=Stegun|editor2-first=Irene A.|editor2-link=Irene Stegun|title=Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables|publisher=[[Dover Publications]]|location=New York|isbn=978-0-486-61272-0|edition=10th|year=1972|title-link=Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables}}, section 4.7., p. 89</ref> Saat ini, fungsi tersebut pada umumnya lebih dikenal sebagai [[fungsi eksponensial]]. |
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! scope="col" |Tanggal |
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! scope="col" |Kategori |
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=== Log tables === |
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! scope="col" |Hasil |
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A key tool that enabled the practical use of logarithms was the ''[[Log table|table of logarithms]]''.<ref>{{Citation|last1=Campbell-Kelly|first1=Martin|title=The history of mathematical tables: from Sumer to spreadsheets|title-link=The History of Mathematical Tables|publisher=[[Oxford University Press]]|series=Oxford scholarship online|isbn=978-0-19-850841-0|year=2003}}, section 2</ref> The first such table was compiled by [[Henry Briggs (mathematician)|Henry Briggs]] in 1617, immediately after Napier's invention but with the innovation of using 10 as the base. Briggs' first table contained the [[Common logarithm|common logarithms]] of all integers in the range from 1 to 1000, with a precision of 14 digits. Subsequently, tables with increasing scope were written. These tables listed the values of {{math|log<sub>10</sub> ''x''}} for any number {{mvar|x}} in a certain range, at a certain precision. Base-10 logarithms were universally used for computation, hence the name common logarithm, since numbers that differ by factors of 10 have logarithms that differ by integers. The common logarithm of {{mvar|x}} can be separated into an [[integer part]] and a [[fractional part]], known as the characteristic and [[Mantissa (logarithm)|mantissa]]. Tables of logarithms need only include the mantissa, as the characteristic can be easily determined by counting digits from the decimal point.<ref>{{Citation|last1=Spiegel|first1=Murray R.|last2=Moyer|first2=R.E.|title=Schaum's outline of college algebra|publisher=[[McGraw-Hill]]|location=New York|series=Schaum's outline series|isbn=978-0-07-145227-4|year=2006}}, p. 264</ref> The characteristic of {{math|10 · {{mvar|x}}}} is one plus the characteristic of {{mvar|x}}, and their mantissas are the same. Thus using a three-digit log table, the logarithm of 3542 is approximated by |
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! scope="col" class="unsortable" |{{Abbr|Ref.|Referensi}} |
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: <math>\log_{10}3542 = \log_{10}(1000 \cdot 3.542) = 3 + \log_{10}3.542 \approx 3 + \log_{10}3.54 \, </math> |
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Greater accuracy can be obtained by [[interpolation]]: |
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: <math>\log_{10}3542 \approx 3 + \log_{10}3.54 + 0.2 (\log_{10}3.55-\log_{10}3.54)\, </math> |
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The value of {{math|10<sup>''x''</sup>}} can be determined by reverse look up in the same table, since the logarithm is a [[monotonic function]]. |
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=== Computations === |
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The product and quotient of two positive numbers {{Mvar|c}} and ''{{Mvar|d}}'' were routinely calculated as the sum and difference of their logarithms. The product {{Math|''cd''}} or quotient {{Math|''c''/''d''}} came from looking up the antilogarithm of the sum or difference, via the same table: |
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: <math> cd = 10^{\, \log_{10} c} \, 10^{\,\log_{10} d} = 10^{\,\log_{10} c \, + \, \log_{10} d}</math> |
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and |
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: <math>\frac c d = c d^{-1} = 10^{\, \log_{10}c \, - \, \log_{10}d}.</math> |
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For manual calculations that demand any appreciable precision, performing the lookups of the two logarithms, calculating their sum or difference, and looking up the antilogarithm is much faster than performing the multiplication by earlier methods such as [[prosthaphaeresis]], which relies on [[trigonometric identities]]. |
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Calculations of powers and [[Nth root|roots]] are reduced to multiplications or divisions and lookups by |
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: <math>c^d = \left(10^{\, \log_{10} c}\right)^d = 10^{\, d \log_{10} c}</math> |
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and |
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: <math>\sqrt[d]{c} = c^\frac{1}{d} = 10^{\frac{1}{d} \log_{10} c}.</math> |
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Trigonometric calculations were facilitated by tables that contained the common logarithms of [[Trigonometric function|trigonometric functions]]. |
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=== Slide rules === |
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Another critical application was the [[slide rule]], a pair of logarithmically divided scales used for calculation. The non-sliding logarithmic scale, [[Gunter's rule]], was invented shortly after Napier's invention. [[William Oughtred]] enhanced it to create the slide rule—a pair of logarithmic scales movable with respect to each other. Numbers are placed on sliding scales at distances proportional to the differences between their logarithms. Sliding the upper scale appropriately amounts to mechanically adding logarithms, as illustrated here: |
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[[Berkas:Slide_rule_example2_with_labels.svg|al=A slide rule: two rectangles with logarithmically ticked axes, arrangement to add the distance from 1 to 2 to the distance from 1 to 3, indicating the product 6.|pus|jmpl|550x550px|Schematic depiction of a slide rule. Starting from 2 on the lower scale, add the distance to 3 on the upper scale to reach the product 6. The slide rule works because it is marked such that the distance from 1 to {{mvar|x}} is proportional to the logarithm of {{mvar|x}}.]] |
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For example, adding the distance from 1 to 2 on the lower scale to the distance from 1 to 3 on the upper scale yields a product of 6, which is read off at the lower part. The slide rule was an essential calculating tool for engineers and scientists until the 1970s, because it allows, at the expense of precision, much faster computation than techniques based on tables.<ref name="ReferenceA">{{Citation|last1=Maor|first1=Eli|title=E: The Story of a Number|publisher=[[Princeton University Press]]|isbn=978-0-691-14134-3|year=2009|at=sections 1, 13}}</ref> |
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== Analytic properties == |
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A deeper study of logarithms requires the concept of a ''[[Function (mathematics)|function]]''. A function is a rule that, given one number, produces another number.<ref>{{citation|last1=Devlin|first1=Keith|author1-link=Keith Devlin|title=Sets, functions, and logic: an introduction to abstract mathematics|publisher=Chapman & Hall/CRC|location=Boca Raton, Fla|edition=3rd|series=Chapman & Hall/CRC mathematics|isbn=978-1-58488-449-1|year=2004|url={{google books |plainurl=y |id=uQHF7bcm4k4C}}}}, or see the references in [[Function (mathematics)|function]]</ref> An example is the function producing the {{mvar|x}}-th power of {{mvar|b}} from any real number {{mvar|x}}, where the base {{mvar|b}} is a fixed number. This function is written as {{math|1=''f''(''x'') = {{mvar|b}}<sup> ''x''</sup>}}. When {{mvar|b}} is positive and unequal to 1, we show below that {{Mvar|f}} is invertible when considered as a function from the reals to the positive reals. |
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=== Existence === |
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Let {{mvar|b}} be a positive real number not equal to 1 and let {{math|1=''f''(''x'') = {{mvar|b}}<sup> ''x''</sup>}}. |
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It is a standard result in real analysis that any continuous strictly monotonic function is bijective between its domain and range. This fact follows from the [[intermediate value theorem]].<ref name="LangIII.3">{{Citation|last1=Lang|first1=Serge|title=Undergraduate analysis|year=1997|series=[[Undergraduate Texts in Mathematics]]|edition=2nd|location=Berlin, New York|publisher=[[Springer-Verlag]]|doi=10.1007/978-1-4757-2698-5|isbn=978-0-387-94841-6|mr=1476913|author1-link=Serge Lang}}, section III.3</ref> Now, {{mvar|f}} is [[Monotonic function|strictly increasing]] (for {{math|''b'' > 1}}), or strictly decreasing (for {{math|0 < {{mvar|b}} < 1}}),<ref name="LangIV.2">{{Harvard citations|last1=Lang|year=1997|nb=yes|loc=section IV.2}}</ref> is continuous, has domain <math>\R</math>, and has range <math>\R_{> 0}</math>. Therefore, {{Mvar|f}} is a bijection from <math>\R</math> to <math>\R_{>0}</math>. In other words, for each positive real number {{Mvar|y}}, there is exactly one real number {{Mvar|x}} such that <math>b^x = y</math>. |
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We let <math>\log_b\colon\R_{>0}\to\R</math> denote the inverse of {{Mvar|f}}. That is, {{math|log<sub>''b''</sub> ''y''}} is the unique real number {{mvar|x}} such that <math>b^x = y</math>. This function is called the base-{{Mvar|b}} ''logarithm function'' or ''logarithmic function'' (or just ''logarithm''). |
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=== Characterization by the product formula === |
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The function {{math|log<sub>''b''</sub> ''x''}} can also be essentially characterized by the product formula |
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: <math>\log_b(xy) = \log_b x + \log_b y.</math> |
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More precisely, the logarithm to any base {{math|''b'' > 1}} is the only [[increasing function]] ''f'' from the positive reals to the reals satisfying {{math|1=''f''(''b'') = 1}} and<ref>{{citation|title=Foundations of Modern Analysis|volume=1|last=Dieudonné|first=Jean|page=84|year=1969|publisher=Academic Press}} item (4.3.1)</ref> |
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: <math>f(xy)=f(x)+f(y).</math> |
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=== Graph of the logarithm function === |
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[[Berkas:Logarithm_inversefunctiontoexp.svg|al=The graphs of two functions.|ka|jmpl|The graph of the logarithm function {{math|log<sub>''b''</sub> (''x'')}} (blue) is obtained by [[Reflection (mathematics)|reflecting]] the graph of the function {{math|''b''<sup>''x''</sup>}} (red) at the diagonal line ({{math|1=''x'' = {{mvar|y}}}}).]] |
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As discussed above, the function {{math|log<sub>''b''</sub>}} is the inverse to the exponential function <math>x\mapsto b^x</math>. Therefore, Their [[Graph of a function|graphs]] correspond to each other upon exchanging the {{mvar|x}}- and the {{mvar|y}}-coordinates (or upon reflection at the diagonal line {{Math|1=''x'' = ''y''}}), as shown at the right: a point {{math|1=(''t'', ''u'' = {{mvar|b}}<sup>''t''</sup>)}} on the graph of {{Mvar|f}} yields a point {{math|1=(''u'', ''t'' = log<sub>''b''</sub> ''u'')}} on the graph of the logarithm and vice versa. As a consequence, {{math|log<sub>''b''</sub> (''x'')}} [[Divergent sequence|diverges to infinity]] (gets bigger than any given number) if {{mvar|x}} grows to infinity, provided that {{mvar|b}} is greater than one. In that case, {{math|log<sub>''b''</sub>(''x'')}} is an [[increasing function]]. For {{math|''b'' < 1}}, {{math|log<sub>''b''</sub> (''x'')}} tends to minus infinity instead. When {{mvar|x}} approaches zero, {{math|log<sub>''b''</sub> ''x''}} goes to minus infinity for {{math|''b'' > 1}} (plus infinity for {{math|''b'' < 1}}, respectively). |
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=== Derivative and antiderivative === |
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[[Berkas:Logarithm_derivative.svg|al=A graph of the logarithm function and a line touching it in one point.|ka|jmpl|220x220px|The graph of the [[natural logarithm]] (green) and its tangent at {{math|''x'' {{=}} 1.5}} (black)]] |
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Analytic properties of functions pass to their inverses.<ref name="LangIII.3" /> Thus, as {{math|1=''f''(''x'') = {{mvar|b}}<sup>''x''</sup>}} is a continuous and [[differentiable function]], so is {{math|log<sub>''b''</sub> ''y''}}. Roughly, a continuous function is differentiable if its graph has no sharp "corners". Moreover, as the [[derivative]] of {{math|''f''(''x'')}} evaluates to {{math|ln(''b'') ''b''<sup>''x''</sup>}} by the properties of the [[exponential function]], the [[chain rule]] implies that the derivative of {{math|log<sub>''b''</sub> ''x''}} is given by<ref name="LangIV.2" /><ref>{{citation|work=Wolfram Alpha|title=Calculation of ''d/dx(Log(b,x))''|publisher=[[Wolfram Research]]|access-date=15 March 2011|url=http://www.wolframalpha.com/input/?i=d/dx(Log(b,x))}}</ref> |
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: <math>\frac{d}{dx} \log_b x = \frac{1}{x\ln b}. </math> |
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That is, the [[slope]] of the [[tangent]] touching the graph of the {{math|base-''b''}} logarithm at the point {{math|(''x'', log<sub>''b''</sub> (''x''))}} equals {{math|1/(''x'' ln(''b''))}}. |
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The derivative of {{Math|ln(''x'')}} is {{Math|1/''x''}}; this implies that {{Math|ln(''x'')}} is the unique [[antiderivative]] of {{math|1/''x''}} that has the value 0 for {{math|1=''x'' = 1}}. It is this very simple formula that motivated to qualify as "natural" the natural logarithm; this is also one of the main reasons of the importance of the [[E (mathematical constant)|constant {{Mvar|e}}]]. |
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The derivative with a generalized functional argument {{math|''f''(''x'')}} is |
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: <math>\frac{d}{dx} \ln f(x) = \frac{f'(x)}{f(x)}.</math> |
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The quotient at the right hand side is called the [[logarithmic derivative]] of ''{{Mvar|f}}''. Computing {{math|''f<nowiki>'</nowiki>''(''x'')}} by means of the derivative of {{math|ln(''f''(''x''))}} is known as [[logarithmic differentiation]].<ref>{{Citation|last1=Kline|first1=Morris|author1-link=Morris Kline|title=Calculus: an intuitive and physical approach|publisher=[[Dover Publications]]|location=New York|series=Dover books on mathematics|isbn=978-0-486-40453-0|year=1998}}, p. 386</ref> The antiderivative of the [[natural logarithm]] {{math|ln(''x'')}} is:<ref>{{citation|work=Wolfram Alpha|title=Calculation of ''Integrate(ln(x))''|publisher=Wolfram Research|access-date=15 March 2011|url=http://www.wolframalpha.com/input/?i=Integrate(ln(x))}}</ref> |
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: <math>\int \ln(x) \,dx = x \ln(x) - x + C.</math> |
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[[List of integrals of logarithmic functions|Related formulas]], such as antiderivatives of logarithms to other bases can be derived from this equation using the change of bases.<ref>{{Harvard citations|editor1-last=Abramowitz|editor2-last=Stegun|year=1972|nb=yes|loc=p. 69}}</ref> |
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=== Integral representation of the natural logarithm === |
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[[Berkas:Natural_logarithm_integral.svg|al=A hyperbola with part of the area underneath shaded in grey.|ka|jmpl|The [[natural logarithm]] of ''{{Mvar|t}}'' is the shaded area underneath the graph of the function {{math|1=''f''(''x'') = 1/''x''}} (reciprocal of {{mvar|x}}).]] |
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The [[natural logarithm]] of {{Mvar|t}} can be defined as the [[definite integral]]: |
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: <math>\ln t = \int_1^t \frac{1}{x} \, dx.</math> |
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This definition has the advantage that it does not rely on the exponential function or any trigonometric functions; the definition is in terms of an integral of a simple reciprocal. As an integral, {{math|ln(''t'')}} equals the area between the {{mvar|x}}-axis and the graph of the function {{math|1/''x''}}, ranging from {{math|1=''x'' = 1}} to {{math|1=''x'' = ''t''}}. This is a consequence of the [[fundamental theorem of calculus]] and the fact that the derivative of {{math|ln(''x'')}} is {{math|1/''x''}}. Product and power logarithm formulas can be derived from this definition.<ref>{{Citation|last1=Courant|first1=Richard|title=Differential and integral calculus. Vol. I|publisher=[[John Wiley & Sons]]|location=New York|series=Wiley Classics Library|isbn=978-0-471-60842-4|mr=1009558|year=1988}}, section III.6</ref> For example, the product formula {{math|1=ln(''tu'') = ln(''t'') + ln(''u'')}} is deduced as: |
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: <math> \ln(tu) = \int_1^{tu} \frac{1}{x} \, dx \ \stackrel {(1)} = \int_1^{t} \frac{1}{x} \, dx + \int_t^{tu} \frac{1}{x} \, dx \ \stackrel {(2)} = \ln(t) + \int_1^u \frac{1}{w} \, dw = \ln(t) + \ln(u).</math> |
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The equality (1) splits the integral into two parts, while the equality (2) is a change of variable ({{math|1=''w'' = {{mvar|x}}/''t''}}). In the illustration below, the splitting corresponds to dividing the area into the yellow and blue parts. Rescaling the left hand blue area vertically by the factor {{Mvar|t}} and shrinking it by the same factor horizontally does not change its size. Moving it appropriately, the area fits the graph of the function {{math|1=''f''(''x'') = 1/''x''}} again. Therefore, the left hand blue area, which is the integral of {{math|''f''(''x'')}} from {{Mvar|t}} to {{Mvar|tu}} is the same as the integral from 1 to {{Mvar|u}}. This justifies the equality (2) with a more geometric proof. |
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[[Berkas:Natural_logarithm_product_formula_proven_geometrically.svg|al=The hyperbola depicted twice. The area underneath is split into different parts.|pus|jmpl|500x500px|A visual proof of the product formula of the natural logarithm]] |
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The power formula {{math|1=ln(''t''<sup>''r''</sup>) = ''r'' ln(''t'')}} may be derived in a similar way: |
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: <math> |
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\ln(t^r) = \int_1^{t^r} \frac{1}{x}dx = \int_1^t \frac{1}{w^r} \left(rw^{r - 1} \, dw\right) = r \int_1^t \frac{1}{w} \, dw = r \ln(t). |
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</math> |
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The second equality uses a change of variables ([[integration by substitution]]), {{math|1=''w'' = {{mvar|x}}<sup>1/''r''</sup>}}. |
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The sum over the reciprocals of natural numbers, |
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: <math>1 + \frac 1 2 + \frac 1 3 + \cdots + \frac 1 n = \sum_{k=1}^n \frac{1}{k},</math> |
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is called the [[Harmonic series (mathematics)|harmonic series]]. It is closely tied to the [[natural logarithm]]: as {{Mvar|n}} tends to [[infinity]], the difference, |
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: <math>\sum_{k=1}^n \frac{1}{k} - \ln(n),</math> |
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[[Limit of a sequence|converges]] (i.e. gets arbitrarily close) to a number known as the [[Euler–Mascheroni constant]] {{math|1=''γ'' = 0.5772...}}. This relation aids in analyzing the performance of algorithms such as [[quicksort]].<ref>{{Citation|last1=Havil|first1=Julian|title=Gamma: Exploring Euler's Constant|publisher=[[Princeton University Press]]|isbn=978-0-691-09983-5|year=2003}}, sections 11.5 and 13.8</ref> |
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=== Transcendence of the logarithm === |
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[[Real number|Real numbers]] that are not [[Algebraic number|algebraic]] are called [[Transcendental number|transcendental]];<ref>{{citation|title=Selected papers on number theory and algebraic geometry|volume=172|first1=Katsumi|last1=Nomizu|author-link=Katsumi Nomizu|location=Providence, RI|publisher=AMS Bookstore|year=1996|isbn=978-0-8218-0445-2|page=21|url={{google books |plainurl=y |id=uDDxdu0lrWAC|page=21}}}}</ref> for example, [[Pi|{{pi}}]] and ''[[E (mathematical constant)|e]]'' are such numbers, but <math>\sqrt{2-\sqrt 3}</math> is not. [[Almost all]] real numbers are transcendental. The logarithm is an example of a [[transcendental function]]. The [[Gelfond–Schneider theorem]] asserts that logarithms usually take transcendental, i.e. "difficult" values.<ref>{{Citation|last1=Baker|first1=Alan|author1-link=Alan Baker (mathematician)|title=Transcendental number theory|publisher=[[Cambridge University Press]]|isbn=978-0-521-20461-3|year=1975}}, p. 10</ref> |
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== Calculation == |
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[[Berkas:Logarithm_keys.jpg|jmpl|The logarithm keys (LOG for base 10 and LN for base {{mvar|e}}) on a [[TI-83 series|TI-83 Plus]] graphing calculator]] |
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Logarithms are easy to compute in some cases, such as {{math|1=log<sub>10</sub> (1000) = 3}}. In general, logarithms can be calculated using [[power series]] or the [[arithmetic–geometric mean]], or be retrieved from a precalculated [[logarithm table]] that provides a fixed precision.<ref>{{Citation|last1=Muller|first1=Jean-Michel|title=Elementary functions|publisher=Birkhäuser Boston|location=Boston, MA|edition=2nd|isbn=978-0-8176-4372-0|year=2006}}, sections 4.2.2 (p. 72) and 5.5.2 (p. 95)</ref><ref>{{Citation|last1=Hart|last2=Cheney|last3=Lawson|year=1968|publisher=John Wiley|location=New York|title=Computer Approximations|series=SIAM Series in Applied Mathematics|display-authors=etal}}, section 6.3, pp. 105–11</ref> [[Newton's method]], an iterative method to solve equations approximately, can also be used to calculate the logarithm, because its inverse function, the exponential function, can be computed efficiently.<ref>{{Citation|last1=Zhang|first1=M.|last2=Delgado-Frias|first2=J.G.|last3=Vassiliadis|first3=S.|title=Table driven Newton scheme for high precision logarithm generation|doi=10.1049/ip-cdt:19941268|journal=IEE Proceedings - Computers and Digital Techniques|issn=1350-2387|volume=141|year=1994|issue=5|pages=281–92}}, section 1 for an overview</ref> Using look-up tables, [[CORDIC]]-like methods can be used to compute logarithms by using only the operations of addition and [[Arithmetic shift|bit shifts]].<ref>{{Citation|url=https://semanticscholar.org/paper/b3741168ba25f23b694cf8f9c80fb4f2aabce513|first=J.E.|last=Meggitt|title=Pseudo Division and Pseudo Multiplication Processes|journal=IBM Journal of Research and Development|date=April 1962|doi=10.1147/rd.62.0210|volume=6|issue=2|pages=210–26|s2cid=19387286}}</ref><ref>{{Citation|last=Kahan|first=W.|author-link=William Kahan|title=Pseudo-Division Algorithms for Floating-Point Logarithms and Exponentials|date=20 May 2001}}</ref> Moreover, the [[Binary logarithm#Algorithm|binary logarithm algorithm]] calculates {{math|lb(''x'')}} [[Recursion|recursively]], based on repeated squarings of {{mvar|x}}, taking advantage of the relation |
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: <math>\log_2\left(x^2\right) = 2 \log_2 |x|.</math> |
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=== Power series === |
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; Taylor series |
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[[Berkas:Taylor_approximation_of_natural_logarithm.gif|al=An animation showing increasingly good approximations of the logarithm graph.|ka|jmpl|The Taylor series of {{math|ln(''z'')}} centered at {{math|''z'' {{=}} 1}}. The animation shows the first 10 approximations along with the 99th and 100th. The approximations do not converge beyond a distance of 1 from the center.]] |
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For any real number {{mvar|z}} that satisfies {{math|0 < ''z'' ≤ 2}}, the following formula holds:{{refn|The same series holds for the principal value of the complex logarithm for complex numbers {{mvar|z}} satisfying {{math|{{!}}''z'' − 1{{!}} < 1}}.|group=nb}}<ref name="AbramowitzStegunp.68">{{Harvard citations|editor1-last=Abramowitz|editor2-last=Stegun|year=1972|nb=yes|loc=p. 68}}</ref> |
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: <math> |
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\begin{align}\ln (z) &= \frac{(z-1)^1}{1} - \frac{(z-1)^2}{2} + \frac{(z-1)^3}{3} - \frac{(z-1)^4}{4} + \cdots \\ |
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&= \sum_{k=1}^\infty (-1)^{k+1}\frac{(z-1)^k}{k} |
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\end{align} |
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</math> |
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This is a shorthand for saying that {{math|ln(''z'')}} can be approximated to a more and more accurate value by the following expressions: |
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: <math> |
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\begin{array}{lllll} |
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(z-1) & & \\ |
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(z-1) & - & \frac{(z-1)^2}{2} & \\ |
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(z-1) & - & \frac{(z-1)^2}{2} & + & \frac{(z-1)^3}{3} \\ |
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\vdots & |
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\end{array} |
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</math> |
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For example, with {{math|''z'' {{=}} 1.5}} the third approximation yields 0.4167, which is about 0.011 greater than {{math|ln(1.5) {{=}} 0.405465}}. This [[Series (mathematics)|series]] approximates {{math|ln(''z'')}} with arbitrary precision, provided the number of summands is large enough. In elementary calculus, {{math|ln(''z'')}} is therefore the [[Limit (mathematics)|limit]] of this series. It is the [[Taylor series]] of the [[natural logarithm]] at {{math|1=''z'' = 1}}. The Taylor series of {{math|ln(''z'')}} provides a particularly useful approximation to {{math|ln(1 + ''z'')}} when {{mvar|z}} is small, {{math|{{!}}''z''{{!}} < 1}}, since then |
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: <math> |
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\ln (1+z) = z - \frac{z^2}{2} +\frac{z^3}{3}\cdots \approx z. |
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</math> |
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For example, with {{math|1=''z'' = 0.1}} the first-order approximation gives {{math|ln(1.1) ≈ 0.1}}, which is less than 5% off the correct value 0.0953. |
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; More efficient series |
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Another series is based on the [[area hyperbolic tangent]] function: |
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: <math> |
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\ln (z) = 2\cdot\operatorname{artanh}\,\frac{z-1}{z+1} = 2 \left ( \frac{z-1}{z+1} + \frac{1}{3}{\left(\frac{z-1}{z+1}\right)}^3 + \frac{1}{5}{\left(\frac{z-1}{z+1}\right)}^5 + \cdots \right ), |
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</math> |
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for any real number {{math|''z'' > 0}}.{{refn|The same series holds for the principal value of the complex logarithm for complex numbers {{mvar|z}} with positive real part.|group=nb}}<ref name="AbramowitzStegunp.68" /> Using [[sigma notation]], this is also written as |
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: <math>\ln (z) = 2\sum_{k=0}^\infty\frac{1}{2k+1}\left(\frac{z-1}{z+1}\right)^{2k+1}.</math> |
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This series can be derived from the above Taylor series. It converges more quickly than the Taylor series, especially if {{mvar|z}} is close to 1. For example, for {{math|1=''z'' = 1.5}}, the first three terms of the second series approximate {{math|ln(1.5)}} with an error of about {{val|3|e=-6}}. The quick convergence for {{mvar|z}} close to 1 can be taken advantage of in the following way: given a low-accuracy approximation {{math|''y'' ≈ ln(''z'')}} and putting |
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: <math>A = \frac z{\exp(y)},</math> |
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the logarithm of {{mvar|z}} is: |
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: <math>\ln (z)=y+\ln (A).</math> |
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The better the initial approximation {{mvar|y}} is, the closer {{mvar|A}} is to 1, so its logarithm can be calculated efficiently. {{mvar|A}} can be calculated using the [[Exponential function|exponential series]], which converges quickly provided {{mvar|y}} is not too large. Calculating the logarithm of larger {{mvar|z}} can be reduced to smaller values of {{mvar|z}} by writing {{math|''z'' {{=}} ''a'' · 10<sup>''b''</sup>}}, so that {{math|ln(''z'') {{=}} ln(''a'') + {{mvar|b}} · ln(10)}}. |
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A closely related method can be used to compute the logarithm of integers. Putting <math>\textstyle z=\frac{n+1}{n}</math> in the above series, it follows that: |
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: <math>\ln (n+1) = \ln(n) + 2\sum_{k=0}^\infty\frac{1}{2k+1}\left(\frac{1}{2 n+1}\right)^{2k+1}.</math> |
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If the logarithm of a large integer {{mvar|n}} is known, then this series yields a fast converging series for {{math|log(''n''+1)}}, with a [[rate of convergence]] of <math display="inline">\left(\frac{1}{2 n+1}\right)^{2}</math>. |
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=== Arithmetic–geometric mean approximation === |
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The [[arithmetic–geometric mean]] yields high precision approximations of the [[natural logarithm]]. Sasaki and Kanada showed in 1982 that it was particularly fast for precisions between 400 and 1000 decimal places, while Taylor series methods were typically faster when less precision was needed. In their work {{math|ln(''x'')}} is approximated to a precision of {{math|2<sup>−''p''</sup>}} (or {{Mvar|p}} precise bits) by the following formula (due to [[Carl Friedrich Gauss]]):<ref>{{Citation|first1=T.|last1=Sasaki|first2=Y.|last2=Kanada|title=Practically fast multiple-precision evaluation of log(x)|journal=Journal of Information Processing|volume=5|issue=4|pages=247–50|year=1982|url=http://ci.nii.ac.jp/naid/110002673332|access-date=30 March 2011}}</ref><ref>{{Citation|first1=Timm|title=Stacs 99|last1=Ahrendt|publisher=Springer|location=Berlin, New York|series=Lecture notes in computer science|doi=10.1007/3-540-49116-3_28|volume=1564|year=1999|pages=302–12|isbn=978-3-540-65691-3|chapter=Fast Computations of the Exponential Function}}</ref> |
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: <math>\ln (x) \approx \frac{\pi}{2\, \mathrm{M}\!\left(1, 2^{2 - m}/x \right)} - m \ln(2).</math> |
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Here {{math|M(''x'', ''y'')}} denotes the [[arithmetic–geometric mean]] of {{mvar|x}} and {{mvar|y}}. It is obtained by repeatedly calculating the average {{Math|(''x'' + ''y'')/2}} ([[arithmetic mean]]) and <math display="inline">\sqrt{xy}</math> ([[geometric mean]]) of {{mvar|x}} and {{mvar|y}} then let those two numbers become the next {{mvar|x}} and {{mvar|y}}. The two numbers quickly converge to a common limit which is the value of {{math|M(''x'', ''y'')}}. {{mvar|m}} is chosen such that |
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: <math>x \,2^m > 2^{p/2}.\, </math> |
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to ensure the required precision. A larger {{mvar|m}} makes the {{math|M(''x'', ''y'')}} calculation take more steps (the initial {{mvar|x}} and {{mvar|y}} are farther apart so it takes more steps to converge) but gives more precision. The constants {{math|{{pi}}}} and {{math|ln(2)}} can be calculated with quickly converging series. |
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=== Feynman's algorithm === |
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While at [[Los Alamos National Laboratory]] working on the [[Manhattan Project]], [[Richard Feynman]] developed a bit-processing algorithm, to compute the logarithm, that is similar to long division and was later used in the [[Connection Machine]]. The algorithm uses the fact that every real number {{Math|1 < ''x'' < 2}} is representable as a product of distinct factors of the form {{Math|1 + 2<sup>−''k''</sup>}}. The algorithm sequentially builds that product {{Mvar|P}}, starting with {{math|''P'' {{=}} 1}} and {{math|''k'' {{=}} 1}}: if {{math|''P'' · (1 + 2<sup>−''k''</sup>) < ''x''}}, then it changes {{Mvar|P}} to {{math|''P'' · (1 + 2<sup>−''k''</sup>)}}. It then increases <math>k</math> by one regardless. The algorithm stops when {{Mvar|k}} is large enough to give the desired accuracy. Because {{Math|log(''x'')}} is the sum of the terms of the form {{Math|log(1 + 2<sup>−''k''</sup>)}} corresponding to those {{Mvar|k}} for which the factor {{Math|1 + 2<sup>−''k''</sup>}} was included in the product {{Mvar|P}}, {{Math|log(''x'')}} may be computed by simple addition, using a table of {{Math|log(1 + 2<sup>−''k''</sup>)}} for all {{Mvar|k}}. Any base may be used for the logarithm table.<ref>{{citation|first=Danny|last=Hillis|author-link=Danny Hillis|title=Richard Feynman and The Connection Machine|journal=Physics Today|volume=42|issue=2|page=78|date=15 January 1989|doi=10.1063/1.881196|bibcode=1989PhT....42b..78H}}</ref> |
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== Applications == |
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[[Berkas:NautilusCutawayLogarithmicSpiral.jpg|al=A photograph of a nautilus' shell.|jmpl|A [[nautilus]] displaying a logarithmic spiral]] |
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Logarithms have many applications inside and outside mathematics. Some of these occurrences are related to the notion of [[scale invariance]]. For example, each chamber of the shell of a [[nautilus]] is an approximate copy of the next one, scaled by a constant factor. This gives rise to a [[logarithmic spiral]].<ref>{{Harvard citations|last1=Maor|year=2009|nb=yes|loc=p. 135}}</ref> [[Benford's law]] on the distribution of leading digits can also be explained by scale invariance.<ref>{{Citation|last1=Frey|first1=Bruce|title=Statistics hacks|publisher=[[O'Reilly Media|O'Reilly]]|location=Sebastopol, CA|series=Hacks Series|url={{google books |plainurl=y |id=HOPyiNb9UqwC|page=275}}|isbn=978-0-596-10164-0|year=2006}}, chapter 6, section 64</ref> Logarithms are also linked to [[self-similarity]]. For example, logarithms appear in the analysis of algorithms that solve a problem by dividing it into two similar smaller problems and patching their solutions.<ref>{{Citation|last1=Ricciardi|first1=Luigi M.|title=Lectures in applied mathematics and informatics|url={{google books |plainurl=y |id=Cw4NAQAAIAAJ}}|publisher=Manchester University Press|location=Manchester|isbn=978-0-7190-2671-3|year=1990}}, p. 21, section 1.3.2</ref> The dimensions of self-similar geometric shapes, that is, shapes whose parts resemble the overall picture are also based on logarithms. [[Logarithmic scale|Logarithmic scales]] are useful for quantifying the relative change of a value as opposed to its absolute difference. Moreover, because the logarithmic function {{math|log(''x'')}} grows very slowly for large {{mvar|x}}, logarithmic scales are used to compress large-scale scientific data. Logarithms also occur in numerous scientific formulas, such as the [[Tsiolkovsky rocket equation]], the [[Fenske equation]], or the [[Nernst equation]]. |
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=== Logarithmic scale === |
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{{Main|Logarithmic scale}} |
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[[Berkas:Germany_Hyperinflation.svg|al=A graph of the value of one mark over time. The line showing its value is increasing very quickly, even with logarithmic scale.|ka|jmpl|A logarithmic chart depicting the value of one [[German gold mark|Goldmark]] in [[German Papiermark|Papiermarks]] during the [[Inflation in the Weimar Republic|German hyperinflation in the 1920s]]]] |
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Scientific quantities are often expressed as logarithms of other quantities, using a ''logarithmic scale''. For example, the [[decibel]] is a [[unit of measurement]] associated with [[logarithmic-scale]] [[Level quantity|quantities]]. It is based on the common logarithm of [[Ratio|ratios]]—10 times the common logarithm of a [[Power (physics)|power]] ratio or 20 times the common logarithm of a [[voltage]] ratio. It is used to quantify the loss of voltage levels in transmitting electrical signals,<ref>{{Citation|last1=Bakshi|first1=U.A.|title=Telecommunication Engineering|publisher=Technical Publications|location=Pune|isbn=978-81-8431-725-1|year=2009|url={{google books |plainurl=y |id=EV4AF0XJO9wC|page=A5}}}}, section 5.2</ref> to describe power levels of sounds in [[acoustics]],<ref>{{Citation|last1=Maling|first1=George C.|editor1-last=Rossing|editor1-first=Thomas D.|title=Springer handbook of acoustics|publisher=[[Springer-Verlag]]|location=Berlin, New York|isbn=978-0-387-30446-5|year=2007|chapter=Noise}}, section 23.0.2</ref> and the [[absorbance]] of light in the fields of [[Spectrometer|spectrometry]] and [[optics]]. The [[signal-to-noise ratio]] describing the amount of unwanted [[Noise (electronic)|noise]] in relation to a (meaningful) [[Signal (information theory)|signal]] is also measured in decibels.<ref>{{Citation|last1=Tashev|first1=Ivan Jelev|title=Sound Capture and Processing: Practical Approaches|publisher=[[John Wiley & Sons]]|location=New York|isbn=978-0-470-31983-3|year=2009|url={{google books |plainurl=y |id=plll9smnbOIC|page=48}}|page=98}}</ref> In a similar vein, the [[peak signal-to-noise ratio]] is commonly used to assess the quality of sound and [[image compression]] methods using the logarithm.<ref>{{Citation|last1=Chui|first1=C.K.|title=Wavelets: a mathematical tool for signal processing|publisher=[[Society for Industrial and Applied Mathematics]]|location=Philadelphia|series=SIAM monographs on mathematical modeling and computation|isbn=978-0-89871-384-8|year=1997|url={{google books |plainurl=y |id=N06Gu433PawC|page=180}}}}</ref> |
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The strength of an earthquake is measured by taking the common logarithm of the energy emitted at the quake. This is used in the [[moment magnitude scale]] or the [[Richter magnitude scale]]. For example, a 5.0 earthquake releases 32 times {{math|(10<sup>1.5</sup>)}} and a 6.0 releases 1000 times {{math|(10<sup>3</sup>)}} the energy of a 4.0.<ref>{{Citation|last1=Crauder|first1=Bruce|last2=Evans|first2=Benny|last3=Noell|first3=Alan|title=Functions and Change: A Modeling Approach to College Algebra|publisher=Cengage Learning|location=Boston|edition=4th|isbn=978-0-547-15669-9|year=2008}}, section 4.4.</ref> [[Apparent magnitude]] measures the brightness of stars logarithmically.<ref>{{Citation|last1=Bradt|first1=Hale|title=Astronomy methods: a physical approach to astronomical observations|publisher=[[Cambridge University Press]]|series=Cambridge Planetary Science|isbn=978-0-521-53551-9|year=2004}}, section 8.3, p. 231</ref> In [[chemistry]] the negative of the decimal logarithm, the decimal '''{{vanchor|cologarithm}}''', is indicated by the letter p.<ref name="Jens">{{cite journal|author=Nørby, Jens|year=2000|title=The origin and the meaning of the little p in pH|journal=Trends in Biochemical Sciences|volume=25|issue=1|pages=36–37|doi=10.1016/S0968-0004(99)01517-0|pmid=10637613}}</ref> For instance, [[pH]] is the decimal cologarithm of the [[Activity (chemistry)|activity]] of [[hydronium]] ions (the form [[hydrogen]] [[Ion|ions]] {{chem|H|+|}} take in water).<ref>{{Citation|author=IUPAC|title=Compendium of Chemical Terminology ("Gold Book")|edition=2nd|editor=A. D. McNaught, A. Wilkinson|publisher=Blackwell Scientific Publications|location=Oxford|year=1997|url=http://goldbook.iupac.org/P04524.html|isbn=978-0-9678550-9-7|doi=10.1351/goldbook|author-link=IUPAC|doi-access=free}}</ref> The activity of hydronium ions in neutral water is 10<sup>−7</sup> [[Molar concentration|mol·L<sup>−1</sup>]], hence a pH of 7. Vinegar typically has a pH of about 3. The difference of 4 corresponds to a ratio of 10<sup>4</sup> of the activity, that is, vinegar's hydronium ion activity is about {{math|10<sup>−3</sup> mol·L<sup>−1</sup>}}. |
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[[Semi-log plot|Semilog]] (log–linear) graphs use the logarithmic scale concept for visualization: one axis, typically the vertical one, is scaled logarithmically. For example, the chart at the right compresses the steep increase from 1 million to 1 trillion to the same space (on the vertical axis) as the increase from 1 to 1 million. In such graphs, [[Exponential function|exponential functions]] of the form {{math|1=''f''(''x'') = ''a'' · ''b''{{i sup|''x''}}}} appear as straight lines with [[slope]] equal to the logarithm of {{mvar|b}}. [[Log-log plot|Log-log]] graphs scale both axes logarithmically, which causes functions of the form {{math|1=''f''(''x'') = ''a'' · ''x''{{i sup|''k''}}}} to be depicted as straight lines with slope equal to the exponent {{mvar|k}}. This is applied in visualizing and analyzing [[Power law|power laws]].<ref>{{Citation|last1=Bird|first1=J.O.|title=Newnes engineering mathematics pocket book|publisher=Newnes|location=Oxford|edition=3rd|isbn=978-0-7506-4992-6|year=2001}}, section 34</ref> |
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=== Psychology === |
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Logarithms occur in several laws describing [[human perception]]:<ref>{{Citation|last1=Goldstein|first1=E. Bruce|title=Encyclopedia of Perception|url={{google books |plainurl=y |id=Y4TOEN4f5ZMC}}|publisher=Sage|location=Thousand Oaks, CA|series=Encyclopedia of Perception|isbn=978-1-4129-4081-8|year=2009}}, pp. 355–56</ref><ref>{{Citation|last1=Matthews|first1=Gerald|title=Human Performance: Cognition, Stress, and Individual Differences|url={{google books |plainurl=y |id=0XrpulSM1HUC}}|publisher=Psychology Press|location=Hove|isbn=978-0-415-04406-6|year=2000}}, p. 48</ref> [[Hick's law]] proposes a logarithmic relation between the time individuals take to choose an alternative and the number of choices they have.<ref>{{Citation|last1=Welford|first1=A.T.|title=Fundamentals of skill|publisher=Methuen|location=London|isbn=978-0-416-03000-6|oclc=219156|year=1968}}, p. 61</ref> [[Fitts's law]] predicts that the time required to rapidly move to a target area is a logarithmic function of the distance to and the size of the target.<ref>{{Citation|author=Paul M. Fitts|date=June 1954|title=The information capacity of the human motor system in controlling the amplitude of movement|journal=Journal of Experimental Psychology|volume=47|issue=6|pages=381–91|pmid=13174710|doi=10.1037/h0055392|s2cid=501599|url=https://semanticscholar.org/paper/3087289229146fc344560478aac366e4977749c0}}, reprinted in {{Citation|journal=Journal of Experimental Psychology: General|volume=121|issue=3|pages=262–69|year=1992|pmid=1402698|url=http://sing.stanford.edu/cs303-sp10/papers/1954-Fitts.pdf|access-date=30 March 2011|title=The information capacity of the human motor system in controlling the amplitude of movement|author=Paul M. Fitts|doi=10.1037/0096-3445.121.3.262}}</ref> In [[psychophysics]], the [[Weber–Fechner law]] proposes a logarithmic relationship between [[Stimulus (psychology)|stimulus]] and [[Sensation (psychology)|sensation]] such as the actual vs. the perceived weight of an item a person is carrying.<ref>{{Citation|last1=Banerjee|first1=J.C.|title=Encyclopaedic dictionary of psychological terms|publisher=M.D. Publications|location=New Delhi|isbn=978-81-85880-28-0|oclc=33860167|year=1994|url={{google books |plainurl=y |id=Pwl5U2q5hfcC|page=306}}|page=304}}</ref> (This "law", however, is less realistic than more recent models, such as [[Stevens's power law]].<ref>{{Citation|last1=Nadel|first1=Lynn|author1-link=Lynn Nadel|title=Encyclopedia of cognitive science|publisher=[[John Wiley & Sons]]|location=New York|isbn=978-0-470-01619-0|year=2005}}, lemmas ''Psychophysics'' and ''Perception: Overview''</ref>) |
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Psychological studies found that individuals with little mathematics education tend to estimate quantities logarithmically, that is, they position a number on an unmarked line according to its logarithm, so that 10 is positioned as close to 100 as 100 is to 1000. Increasing education shifts this to a linear estimate (positioning 1000 10 times as far away) in some circumstances, while logarithms are used when the numbers to be plotted are difficult to plot linearly.<ref>{{Citation|doi=10.1111/1467-9280.02438|journal=Psychological Science|archive-date=17 May 2011|archive-url=https://web.archive.org/web/20110517002232/http://www.psy.cmu.edu/~siegler/sieglerbooth-cd04.pdf|access-date=7 January 2011|s2cid=9583202|citeseerx=10.1.1.727.3696|pmid=12741747|url=http://www.psy.cmu.edu/~siegler/sieglerbooth-cd04.pdf|year=2003|last1=Siegler|pages=237–43|issue=3|volume=14|title=The Development of Numerical Estimation. Evidence for Multiple Representations of Numerical Quantity|first2=John E.|last2=Opfer|first1=Robert S.|url-status=dead}}</ref><ref>{{Citation|last1=Dehaene|issue=5880|bibcode=2008Sci...320.1217D|journal=Science|year=2008|pmid=18511690|pmc=2610411|doi=10.1126/science.1156540|pages=1217–20|volume=320|first1=Stanislas|title=Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures|first4=Pierre|last4=Pica|first3=Elizabeth|last3=Spelke|first2=Véronique|last2=Izard|citeseerx=10.1.1.362.2390}}</ref> |
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=== Probability theory and statistics === |
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[[Berkas:PDF-log_normal_distributions.svg|al=Three asymmetric PDF curves|ka|jmpl|Three [[Probability density function|probability density functions]] (PDF) of random variables with log-normal distributions. The location parameter {{math|μ}}, which is zero for all three of the PDFs shown, is the mean of the logarithm of the random variable, not the mean of the variable itself.]] |
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[[Berkas:Benfords_law_illustrated_by_world's_countries_population.png|al=A bar chart and a superimposed second chart. The two differ slightly, but both decrease in a similar fashion.|ka|jmpl|Distribution of first digits (in %, red bars) in the [[List of countries by population|population of the 237 countries]] of the world. Black dots indicate the distribution predicted by Benford's law.]] |
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Logarithms arise in [[probability theory]]: the [[law of large numbers]] dictates that, for a [[fair coin]], as the number of coin-tosses increases to infinity, the observed proportion of heads [[Binomial distribution|approaches one-half]]. The fluctuations of this proportion about one-half are described by the [[law of the iterated logarithm]].<ref>{{Citation|last1=Breiman|first1=Leo|title=Probability|publisher=[[Society for Industrial and Applied Mathematics]]|location=Philadelphia|series=Classics in applied mathematics|isbn=978-0-89871-296-4|year=1992}}, section 12.9</ref> |
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Logarithms also occur in [[Log-normal distribution|log-normal distributions]]. When the logarithm of a [[random variable]] has a [[normal distribution]], the variable is said to have a log-normal distribution.<ref>{{Citation|last1=Aitchison|first1=J.|last2=Brown|first2=J.A.C.|title=The lognormal distribution|publisher=[[Cambridge University Press]]|isbn=978-0-521-04011-2|oclc=301100935|year=1969}}</ref> Log-normal distributions are encountered in many fields, wherever a variable is formed as the product of many independent positive random variables, for example in the study of turbulence.<ref>{{Citation|title=An introduction to turbulent flow|author=Jean Mathieu and Julian Scott|publisher=Cambridge University Press|year=2000|isbn=978-0-521-77538-0|page=50|url={{google books |plainurl=y |id=nVA53NEAx64C|page=50}}}}</ref> |
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Logarithms are used for [[maximum-likelihood estimation]] of parametric [[Statistical model|statistical models]]. For such a model, the [[likelihood function]] depends on at least one [[Parametric model|parameter]] that must be estimated. A maximum of the likelihood function occurs at the same parameter-value as a maximum of the logarithm of the likelihood (the "''log likelihood''"), because the logarithm is an increasing function. The log-likelihood is easier to maximize, especially for the multiplied likelihoods for [[Independence (probability)|independent]] random variables.<ref>{{Citation|last1=Rose|first1=Colin|last2=Smith|first2=Murray D.|title=Mathematical statistics with Mathematica|publisher=[[Springer-Verlag]]|location=Berlin, New York|series=Springer texts in statistics|isbn=978-0-387-95234-5|year=2002}}, section 11.3</ref> |
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[[Benford's law]] describes the occurrence of digits in many [[Data set|data sets]], such as heights of buildings. According to Benford's law, the probability that the first decimal-digit of an item in the data sample is {{Mvar|d}} (from 1 to 9) equals {{math|log<sub>10</sub> (''d'' + 1) − log<sub>10</sub> (''d'')}}, ''regardless'' of the unit of measurement.<ref>{{Citation|last1=Tabachnikov|first1=Serge|author-link1=Sergei Tabachnikov|title=Geometry and Billiards|publisher=[[American Mathematical Society]]|location=Providence, RI|isbn=978-0-8218-3919-5|year=2005|pages=36–40}}, section 2.1</ref> Thus, about 30% of the data can be expected to have 1 as first digit, 18% start with 2, etc. Auditors examine deviations from Benford's law to detect fraudulent accounting.<ref>{{citation|title=The Effective Use of Benford's Law in Detecting Fraud in Accounting Data|first1=Cindy|last1=Durtschi|first2=William|last2=Hillison|first3=Carl|last3=Pacini|url=http://faculty.usfsp.edu/gkearns/Articles_Fraud/Benford%20Analysis%20Article.pdf|volume=V|pages=17–34|year=2004|journal=Journal of Forensic Accounting|archive-url=https://web.archive.org/web/20170829062510/http://faculty.usfsp.edu/gkearns/Articles_Fraud/Benford%20Analysis%20Article.pdf|archive-date=29 August 2017|access-date=28 May 2018}}</ref> |
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=== Computational complexity === |
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[[Analysis of algorithms]] is a branch of [[computer science]] that studies the [[Time complexity|performance]] of [[Algorithm|algorithms]] (computer programs solving a certain problem).<ref name="Wegener">{{Citation|last1=Wegener|first1=Ingo|title=Complexity theory: exploring the limits of efficient algorithms|publisher=[[Springer-Verlag]]|location=Berlin, New York|isbn=978-3-540-21045-0|year=2005}}, pp. 1–2</ref> Logarithms are valuable for describing algorithms that [[Divide and conquer algorithm|divide a problem]] into smaller ones, and join the solutions of the subproblems.<ref>{{Citation|last1=Harel|first1=David|last2=Feldman|first2=Yishai A.|title=Algorithmics: the spirit of computing|location=New York|publisher=[[Addison-Wesley]]|isbn=978-0-321-11784-7|year=2004}}, p. 143</ref> |
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For example, to find a number in a sorted list, the [[binary search algorithm]] checks the middle entry and proceeds with the half before or after the middle entry if the number is still not found. This algorithm requires, on average, {{math|log<sub>2</sub> (''N'')}} comparisons, where {{mvar|N}} is the list's length.<ref>{{citation|last=Knuth|first=Donald|author-link=Donald Knuth|title=The Art of Computer Programming|publisher=Addison-Wesley|location=Reading, MA|year=1998|isbn=978-0-201-89685-5|title-link=The Art of Computer Programming}}, section 6.2.1, pp. 409–26</ref> Similarly, the [[merge sort]] algorithm sorts an unsorted list by dividing the list into halves and sorting these first before merging the results. Merge sort algorithms typically require a time [[Big O notation|approximately proportional to]] {{math|''N'' · log(''N'')}}.<ref>{{Harvard citations|last=Knuth|first=Donald|year=1998|loc=section 5.2.4, pp. 158–68|nb=yes}}</ref> The base of the logarithm is not specified here, because the result only changes by a constant factor when another base is used. A constant factor is usually disregarded in the analysis of algorithms under the standard [[uniform cost model]].<ref name="Wegener20">{{Citation|last1=Wegener|first1=Ingo|title=Complexity theory: exploring the limits of efficient algorithms|publisher=[[Springer-Verlag]]|location=Berlin, New York|isbn=978-3-540-21045-0|year=2005|page=20}}</ref> |
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A function {{math|''f''(''x'')}} is said to [[Logarithmic growth|grow logarithmically]] if {{math|''f''(''x'')}} is (exactly or approximately) proportional to the logarithm of {{mvar|x}}. (Biological descriptions of organism growth, however, use this term for an exponential function.<ref>{{Citation|last1=Mohr|first1=Hans|last2=Schopfer|first2=Peter|title=Plant physiology|publisher=Springer-Verlag|location=Berlin, New York|isbn=978-3-540-58016-4|year=1995|url-access=registration|url=https://archive.org/details/plantphysiology0000mohr}}, chapter 19, p. 298</ref>) For example, any [[natural number]] {{mvar|N}} can be represented in [[Binary numeral system|binary form]] in no more than {{math|log<sub>2</sub> ''N'' + 1}} [[Bit|bits]]. In other words, the amount of [[Memory (computing)|memory]] needed to store {{mvar|N}} grows logarithmically with {{mvar|N}}. |
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=== Entropy and chaos === |
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[[Berkas:Chaotic_Bunimovich_stadium.png|al=An oval shape with the trajectories of two particles.|ka|jmpl|[[Dynamical billiards|Billiards]] on an oval [[billiard table]]. Two particles, starting at the center with an angle differing by one degree, take paths that diverge chaotically because of [[Reflection (physics)|reflections]] at the boundary.]] |
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[[Entropy]] is broadly a measure of the disorder of some system. In [[statistical thermodynamics]], the entropy ''S'' of some physical system is defined as |
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: <math> S = - k \sum_i p_i \ln(p_i).\, </math> |
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The sum is over all possible states {{Mvar|i}} of the system in question, such as the positions of gas particles in a container. Moreover, {{math|''p''<sub>''i''</sub>}} is the probability that the state {{Mvar|i}} is attained and {{mvar|k}} is the [[Boltzmann constant]]. Similarly, [[Entropy (information theory)|entropy in information theory]] measures the quantity of information. If a message recipient may expect any one of {{mvar|N}} possible messages with equal likelihood, then the amount of information conveyed by any one such message is quantified as {{math|log<sub>2</sub> ''N''}} bits.<ref>{{Citation|last1=Eco|first1=Umberto|author1-link=Umberto Eco|title=The open work|publisher=[[Harvard University Press]]|isbn=978-0-674-63976-8|year=1989}}, section III.I</ref> |
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[[Lyapunov exponent|Lyapunov exponents]] use logarithms to gauge the degree of chaoticity of a [[dynamical system]]. For example, for a particle moving on an oval billiard table, even small changes of the initial conditions result in very different paths of the particle. Such systems are [[Chaos theory|chaotic]] in a [[Deterministic system|deterministic]] way, because small measurement errors of the initial state predictably lead to largely different final states.<ref>{{Citation|last1=Sprott|first1=Julien Clinton|title=Elegant Chaos: Algebraically Simple Chaotic Flows|journal=Elegant Chaos: Algebraically Simple Chaotic Flows. Edited by Sprott Julien Clinton. Published by World Scientific Publishing Co. Pte. Ltd|url={{google books |plainurl=y |id=buILBDre9S4C}}|publisher=[[World Scientific]]|location=New Jersey|isbn=978-981-283-881-0|year=2010|bibcode=2010ecas.book.....S|doi=10.1142/7183}}, section 1.9</ref> At least one Lyapunov exponent of a deterministically chaotic system is positive. |
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=== Fractals === |
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[[Berkas:Sierpinski_dimension.svg|al=Parts of a triangle are removed in an iterated way.|ka|jmpl|400x400px|The Sierpinski triangle (at the right) is constructed by repeatedly replacing [[Equilateral triangle|equilateral triangles]] by three smaller ones.]] |
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Logarithms occur in definitions of the [[Fractal dimension|dimension]] of [[Fractal|fractals]].<ref>{{Citation|last1=Helmberg|first1=Gilbert|title=Getting acquainted with fractals|publisher=Walter de Gruyter|series=De Gruyter Textbook|location=Berlin, New York|isbn=978-3-11-019092-2|year=2007}}</ref> Fractals are geometric objects that are self-similar in the sense that small parts reproduce, at least roughly, the entire global structure. The [[Sierpinski triangle]] (pictured) can be covered by three copies of itself, each having sides half the original length. This makes the [[Hausdorff dimension]] of this structure {{math|ln(3)/ln(2) ≈ 1.58}}. Another logarithm-based notion of dimension is obtained by [[Box-counting dimension|counting the number of boxes]] needed to cover the fractal in question. |
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=== Music === |
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{{multiple image |
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| direction = vertical |
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| width = 350 |
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| footer = Four different octaves shown on a linear scale, then shown on a logarithmic scale (as the ear hears them). |
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| image1 = 4Octaves.and.Frequencies.svg |
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| alt1 = Four different octaves shown on a linear scale. |
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| image2 = 4Octaves.and.Frequencies.Ears.svg |
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| alt2 = Four different octaves shown on a logarithmic scale. |
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}} |
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Logarithms are related to musical tones and [[Interval (music)|intervals]]. In [[equal temperament]], the frequency ratio depends only on the interval between two tones, not on the specific frequency, or [[Pitch (music)|pitch]], of the individual tones. For example, the [[A (musical note)|note ''A'']] has a frequency of 440 [[Hertz|Hz]] and [[B♭ (musical note)|''B-flat'']] has a frequency of 466 Hz. The interval between ''A'' and ''B-flat'' is a [[semitone]], as is the one between ''B-flat'' and [[B (musical note)|''B'']] (frequency 493 Hz). Accordingly, the frequency ratios agree: |
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: <math>\frac{466}{440} \approx \frac{493}{466} \approx 1.059 \approx \sqrt[12]2.</math> |
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Therefore, logarithms can be used to describe the intervals: an interval is measured in semitones by taking the {{Nowrap|base-{{math|2<sup>1/12</sup>}}}} logarithm of the [[frequency]] ratio, while the {{Nowrap|base-{{math|2<sup>1/1200</sup>}}}} logarithm of the frequency ratio expresses the interval in [[Cent (music)|cents]], hundredths of a semitone. The latter is used for finer encoding, as it is needed for non-equal temperaments.<ref>{{Citation|last1=Wright|first1=David|title=Mathematics and music|location=Providence, RI|publisher=AMS Bookstore|isbn=978-0-8218-4873-9|year=2009}}, chapter 5</ref> |
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{| class="wikitable" style="text-align:center; margin:1em auto 1em auto;" |
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|'''Interval'''(the two tones are played at the same time) |
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|[[72 tone equal temperament|1/12 tone]] {{audio|1_step_in_72-et_on_C.mid|play}} |
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|[[Semitone]] {{audio|Minor_second_on_C.mid|play|help=no}} |
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|[[Just major third]] {{audio|Just_major_third_on_C.mid|play|help=no}} |
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|[[Major third]] {{audio|Major_third_on_C.mid|play|help=no}} |
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|[[Tritone]] {{audio|Tritone_on_C.mid|play|help=no}} |
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|[[Octave]] {{audio|Perfect_octave_on_C.mid|play|help=no}} |
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|[[Golden Joystick Awards#2020|Golden Joystick 2020]] |
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|'''Frequency ratio''' ''r'' |
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|24 November 2020 |
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|<math>2^{\frac 1 {72}} \approx 1.0097</math> |
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|Breakthrough Award|{{won}} |
|||
|<math>2^{\frac 1 {12}} \approx 1.0595</math> |
|||
| style="text-align:center;" |<ref>{{cite web|last=Tyrer|first=Ben|date=November 24, 2020|title=Among Us developer wins this year's Breakthrough Award at the Golden Joysticks|url=https://www.gamesradar.com/uk/among-us-developer-wins-this-years-breakthrough-award-at-the-golden-joysticks/|website=GamesRadar+|archive-url=https://web.archive.org/web/20201128113314/https://www.gamesradar.com/uk/among-us-developer-wins-this-years-breakthrough-award-at-the-golden-joysticks/|archive-date=November 28, 2020|access-date=November 28, 2020|url-status=live}}</ref> |
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|<math>\tfrac 5 4 = 1.25</math> |
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|<math>\begin{align} 2^{\frac 4 {12}} & = \sqrt[3] 2 \\ & \approx 1.2599 \end{align} </math> |
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|<math>\begin{align} 2^{\frac 6 {12}} & = \sqrt 2 \\ & \approx 1.4142 \end{align} </math> |
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|<math> 2^{\frac {12} {12}} = 2 </math> |
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|- |
|- |
||
| rowspan="2" scope="row" |[[The Game Awards 2020]] |
|||
|'''Corresponding number of semitones'''<math>\log_{\sqrt[12] 2}(r) = 12 \log_2 (r)</math> |
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| rowspan="2" |10 Desember 2020 |
|||
|<math>\tfrac 1 6</math> |
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|Best Mobile Game|{{won}} |
|||
|<math>1</math> |
|||
| rowspan="2" style="text-align:center;" |<ref>{{cite web|last=Makuch|first=Eddie|date=November 18, 2020|title=New Among Us Map Teased, Announcement Coming At The Game Awards|url=https://www.gamespot.com/articles/new-among-us-map-teased-announcement-coming-at-the-game-awards/1100-6484604/|website=GameSpot|archive-url=https://web.archive.org/web/20201119152145/https://www.gamespot.com/articles/new-among-us-map-teased-announcement-coming-at-the-game-awards/1100-6484604/|archive-date=November 19, 2020|access-date=November 19, 2020|url-status=live}}</ref><ref>{{Cite web|last=Ryan|first=Jackson|date=December 10, 2020|title=The Game Awards 2020: Every result, winner, world premiere, trailers and more|url=https://www.cnet.com/news/the-game-awards-2020-every-result-winner-world-premiere-trailers-and-more/|website=CNET|language=en|archive-url=https://web.archive.org/web/20201211033532/https://www.cnet.com/news/the-game-awards-2020-every-result-winner-world-premiere-trailers-and-more/|archive-date=December 11, 2020|access-date=December 11, 2020|url-status=live}}</ref> |
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|<math>\approx 3.8631</math> |
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|<math>4</math> |
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|<math>6</math> |
|||
|<math>12</math> |
|||
|- |
|- |
||
|Best Multiplayer Game|{{won}} |
|||
|'''Corresponding number of cents'''<math>\log_{\sqrt[1200] 2}(r) = 1200 \log_2 (r)</math> |
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|- |
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|<math>16 \tfrac 2 3</math> |
|||
|[[Steam Awards#2020|Steam Awards 2020]] |
|||
|<math>100</math> |
|||
|3 Januari 2021 |
|||
|<math>\approx 386.31</math> |
|||
|Labor of Love Award|{{nominated}} |
|||
|<math>400</math> |
|||
| style="text-align:center;" |<ref>{{cite web|author=Izaak|date=December 20, 2020|title=Steam Awards 2020 nominees revealed|url=https://www.sportskeeda.com/esports/news-steam-awards-2020-nominees-revealed|website=Sportskeeda|access-date=November 19, 2020|url-status=live}}</ref><ref>{{cite web|date=January 3, 2021|title=The Steam Awards|url=https://store.steampowered.com/steamawards|work=Steam|archive-url=https://web.archive.org/web/20210124061809/https://store.steampowered.com/steamawards/|archive-date=January 24, 2021|access-date=January 27, 2021|url-status=live}}</ref> |
|||
|<math>600</math> |
|||
|- |
|||
|<math>1200</math> |
|||
|[[2021 Kids' Choice Awards|Nickelodeon Kids' Choice Awards]] |
|||
|13 Maret 2021 |
|||
|Favorite Video Game|{{won}} |
|||
| style="text-align:center" |<ref>{{cite web|author=Liz Calvario|date=March 13, 2021|title=2021 Kids' Choice Awards: The Complete Winners List|url=https://www.etonline.com/2021-kids-choice-awards-the-complete-winners-list-161949|work=[[Entertainment Tonight]]|access-date=March 13, 2021}}</ref> |
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|} |
|||
{| class="wikitable plainrowheaders sortable" width="auto" |
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! scope="col" |Award |
|||
! scope="col" |Date of ceremony |
|||
! scope="col" |Category |
|||
! scope="col" |Result |
|||
! scope="col" class="unsortable" |{{Abbr|Ref.|References}} |
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|- |
|||
|[[Golden Joystick Awards#2020|Golden Joystick Awards 2020]] |
|||
|November 24, 2020 |
|||
|Breakthrough Award|{{won}} |
|||
| style="text-align:center;" |<ref>{{cite web|last=Tyrer|first=Ben|date=November 24, 2020|title=Among Us developer wins this year's Breakthrough Award at the Golden Joysticks|url=https://www.gamesradar.com/uk/among-us-developer-wins-this-years-breakthrough-award-at-the-golden-joysticks/|website=GamesRadar+|archive-url=https://web.archive.org/web/20201128113314/https://www.gamesradar.com/uk/among-us-developer-wins-this-years-breakthrough-award-at-the-golden-joysticks/|archive-date=November 28, 2020|access-date=November 28, 2020|url-status=live}}</ref> |
|||
|- |
|||
| rowspan="2" scope="row" |[[The Game Awards 2020]] |
|||
| rowspan="2" |December 10, 2020 |
|||
|Best Mobile Game|{{won}} |
|||
| rowspan="2" style="text-align:center;" |<ref>{{cite web|last=Makuch|first=Eddie|date=November 18, 2020|title=New Among Us Map Teased, Announcement Coming At The Game Awards|url=https://www.gamespot.com/articles/new-among-us-map-teased-announcement-coming-at-the-game-awards/1100-6484604/|website=GameSpot|archive-url=https://web.archive.org/web/20201119152145/https://www.gamespot.com/articles/new-among-us-map-teased-announcement-coming-at-the-game-awards/1100-6484604/|archive-date=November 19, 2020|access-date=November 19, 2020|url-status=live}}</ref><ref>{{Cite web|last=Ryan|first=Jackson|date=December 10, 2020|title=The Game Awards 2020: Every result, winner, world premiere, trailers and more|url=https://www.cnet.com/news/the-game-awards-2020-every-result-winner-world-premiere-trailers-and-more/|website=CNET|language=en|archive-url=https://web.archive.org/web/20201211033532/https://www.cnet.com/news/the-game-awards-2020-every-result-winner-world-premiere-trailers-and-more/|archive-date=December 11, 2020|access-date=December 11, 2020|url-status=live}}</ref> |
|||
|- |
|||
|Best Multiplayer Game|{{won}} |
|||
|- |
|||
|[[Steam Awards#2020|Steam Awards 2020]] |
|||
|January 3, 2021 |
|||
|Labor of Love Award|{{nominated}} |
|||
| style="text-align:center;" |<ref>{{cite web|author=Izaak|date=December 20, 2020|title=Steam Awards 2020 nominees revealed|url=https://www.sportskeeda.com/esports/news-steam-awards-2020-nominees-revealed|website=Sportskeeda|access-date=November 19, 2020}}</ref><ref>{{cite web|date=January 3, 2021|title=The Steam Awards|url=https://store.steampowered.com/steamawards/2020|work=Steam|archive-url=https://web.archive.org/web/20210124061809/https://store.steampowered.com/steamawards/|archive-date=January 24, 2021|access-date=January 27, 2021|url-status=live}}</ref> |
|||
|- |
|||
|[[2021 Kids' Choice Awards|Nickelodeon Kids' Choice Awards]] |
|||
|March 13, 2021 |
|||
|Favorite Video Game|{{won}} |
|||
| style="text-align:center" |<ref>{{cite web|author=Liz Calvario|date=March 13, 2021|title=2021 Kids' Choice Awards: The Complete Winners List|url=https://www.etonline.com/2021-kids-choice-awards-the-complete-winners-list-161949|work=[[Entertainment Tonight]]|access-date=March 13, 2021}}</ref> |
|||
|- |
|||
|[[Webby Awards|Webby Awards 2021]] |
|||
|May 18, 2021 |
|||
|Breakout of the Year|{{won}} |
|||
| style="text-align:center;" |<ref>{{Cite web|title=Among Us|url=http://winners.webbyawards.com/2021/specialachievement/280/among-us|website=[[Webby Awards|The Webby Awards]]|language=en|access-date=2021-06-15}}</ref><ref>{{Cite web|title=WINNERS ANNOUNCED FOR THE 25TH ANNUAL WEBBY AWARDS {{!}} The Webby Awards|url=https://www.webbyawards.com/press/press-releases/winners-announced-for-the-25th-annual-webby-awards/|website=[[Webby Awards|The Webby Awards]]|language=en-US|access-date=2021-10-25}}</ref> |
|||
|- |
|||
|Mobile Games Awards |
|||
|July 20, 2021 |
|||
|Best Indie Developer|{{won}} |
|||
| style="text-align:center;" |<ref>{{cite web|title=Mobile Games Awards on Twitter|url=https://twitter.com/MobileGameAward/status/1417561841023213569|language=en|access-date=2022-04-03}}</ref><ref>{{cite web|title=The Winners of 2021 - Mobile Games Awards|url=https://www.mobilegamesawards.com/the-winners-of-2021|language=en}}</ref> |
|||
|- |
|||
|[[International Game Developers Association]] |
|||
|August 27, 2021 |
|||
|Community Management|{{won}} |
|||
| style="text-align:center;" |<ref>{{Cite web|date=August 27, 2021|title=International Game Developers Association (IGDA)|url=https://twitter.com/IGDA/status/1431325675533881349|website=[[International Game Developers Association]]|language=en|access-date=2022-04-03}}</ref> |
|||
|- |
|||
|App Store Awards |
|||
|December 2, 2021 |
|||
|Connections|{{won}} |
|||
| style="text-align:center;" |<ref>{{Cite web|date=December 2, 2021|title=Announcing the App Store Award Winners - The 15 best apps and games of 2021|url=https://apps.apple.com/story/id1591083005|language=en|access-date=2022-04-03}}</ref> |
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|- |
|||
|[[British Academy Games Awards]] |
|||
|April 7, 2022 |
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|Evolving Game|{{nominated}} |
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| style="text-align:center;" |<ref>{{Cite web|title=BAFTA 2022|url=https://www.bafta.org/games/awards/2022-nominations-winners#evolving-game|website=[[British Academy Games Awards]]|language=en|access-date=2022-04-03}}</ref> |
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|} |
|} |
||
=== |
=== Warisan === |
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''Among Us'' has done collaborations and cross-overs with other games and studios. The first game they collaborated with was ''[[Fall Guys]]'', who added ''Among Us''-themed skins to their game.<ref>{{cite web|last=Parrish|first=Ash|date=June 30, 2021|title=Fall Guys' Latest Costume Is Very Suspicious|url=https://kotaku.com/fall-guys-latest-costume-is-very-suspicious-1847203622|work=[[Kotaku]]|access-date=August 18, 2021}}</ref> Characters from ''Among Us'' have made cameos in the indie games ''[[Astroneer]]'',<ref>{{cite web|date=July 29, 2021|title=ASTRONEER on Twitter|url=https://twitter.com/astroneergame/status/1420750234309652482|access-date=2022-04-03}}</ref> ''Sunshine Heavy Industries'',<ref>{{cite web|date=October 8, 2021|title=Version 1.1.3 - Among Us crossover mission; dirty engine rebalance|url=https://store.steampowered.com/news/app/1542810/view/3037106866327440897|access-date=2022-04-03}}</ref> ''[[Cosmonious High]]'',<ref>{{cite web|date=March 25, 2022|title=Among Us Crewmate Enters 3D World Of Cosmonious High In New Collab|url=https://www.gamespot.com/articles/among-us-crewmate-enters-3d-world-of-cosmonious-high-in-new-collab/1100-6501905/|work=[[GameSpot]]|access-date=2022-04-04}}</ref> and ''[[Samurai Gunn|Samurai Gunn 2]]'',<ref>{{cite web|date=December 16, 2021|title=Samurai Gunn 2 × Among Us update is now live!|url=https://store.steampowered.com/news/app/1397790/view/3114800084600284276|access-date=2022-04-03}}</ref> and ''Among Us'' is referenced in several stickers in the game ''[[A Hat in Time]]''.<ref>{{cite web|date=March 4, 2022|title=A Hat in Time on Twitter|url=https://twitter.com/HatInTime/status/1499791852089888771|access-date=2022-04-03}}</ref> Several ''Among Us''-themed cards are included in ''[[The Binding of Isaac: Four Souls#Requiem Expansion|The Binding of Isaac: Four Souls Requiem]]''.<ref>{{cite web|date=June 24, 2021|title=Among Us Invades Binding Of Isaac: Four Souls With Crossover Cards|url=https://screenrant.com/among-us-binding-isaac-four-souls-crossover-cards/|work=[[Screen Rant]]|access-date=2022-04-03}}</ref> |
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[[Natural logarithm|Natural logarithms]] are closely linked to [[Prime-counting function|counting prime numbers]] (2, 3, 5, 7, 11, ...), an important topic in [[number theory]]. For any [[integer]] {{mvar|x}}, the quantity of [[Prime number|prime numbers]] less than or equal to {{mvar|x}} is denoted {{math|[[prime-counting function|{{pi}}(''x'')]]}}. The [[prime number theorem]] asserts that {{math|{{pi}}(''x'')}} is approximately given by |
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: <math>\frac{x}{\ln(x)},</math> |
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in the sense that the ratio of {{math|{{pi}}(''x'')}} and that fraction approaches 1 when {{mvar|x}} tends to infinity.<ref>{{Citation|last1=Bateman|first1=P.T.|last2=Diamond|first2=Harold G.|title=Analytic number theory: an introductory course|publisher=[[World Scientific]]|location=New Jersey|isbn=978-981-256-080-3|oclc=492669517|year=2004}}, theorem 4.1</ref> As a consequence, the probability that a randomly chosen number between 1 and {{mvar|x}} is prime is inversely [[Proportionality (mathematics)|proportional]] to the number of decimal digits of {{mvar|x}}. A far better estimate of {{math|{{pi}}(''x'')}} is given by the [[Logarithmic integral function|offset logarithmic integral]] function {{math|Li(''x'')}}, defined by |
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: <math> \mathrm{Li}(x) = \int_2^x \frac1{\ln(t)} \,dt. </math> |
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The [[Riemann hypothesis]], one of the oldest open mathematical [[Conjecture|conjectures]], can be stated in terms of comparing {{math|{{pi}}(''x'')}} and {{math|Li(''x'')}}.<ref>{{Harvard citations|last1=Bateman|first1=P. T.|last2=Diamond|year=2004|nb=yes|loc=Theorem 8.15}}</ref> The [[Erdős–Kac theorem]] describing the number of distinct [[Prime factor|prime factors]] also involves the [[natural logarithm]]. |
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The logarithm of ''n'' [[factorial]], {{math|1=''n''! = 1 · 2 · ... · ''n''}}, is given by |
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: <math> \ln (n!) = \ln (1) + \ln (2) + \cdots + \ln (n).</math> |
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This can be used to obtain [[Stirling's formula]], an approximation of {{math|''n''!}} for large {{mvar|n}}.<ref>{{Citation|last1=Slomson|first1=Alan B.|title=An introduction to combinatorics|publisher=[[CRC Press]]|location=London|isbn=978-0-412-35370-3|year=1991}}, chapter 4</ref> |
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== Generalizations == |
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=== Complex logarithm === |
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{{Main|Complex logarithm}} |
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[[Berkas:Complex_number_illustration_multiple_arguments.svg|al=An illustration of the polar form: a point is described by an arrow or equivalently by its length and angle to the x-axis.|ka|jmpl|Polar form of {{math|''z {{=}} x + iy''}}. Both {{mvar|φ}} and {{mvar|φ'}} are arguments of {{mvar|z}}.]] |
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All the [[Complex number|complex numbers]] {{mvar|a}} that solve the equation |
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: <math>e^a=z</math> |
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are called ''complex logarithms'' of {{mvar|z}}, when {{mvar|z}} is (considered as) a complex number. A complex number is commonly represented as {{math|''z {{=}} x + iy''}}, where {{mvar|x}} and {{mvar|y}} are real numbers and {{mvar|i}} is an [[imaginary unit]], the square of which is −1. Such a number can be visualized by a point in the [[complex plane]], as shown at the right. The [[polar form]] encodes a non-zero complex number {{mvar|z}} by its [[absolute value]], that is, the (positive, real) distance {{Mvar|r}} to the [[Origin (mathematics)|origin]], and an angle between the real ({{mvar|x}}) axis'' ''{{Math|Re}} and the line passing through both the origin and {{mvar|z}}. This angle is called the [[Argument (complex analysis)|argument]] of {{mvar|z}}. |
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The absolute value {{mvar|r}} of {{mvar|z}} is given by |
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: <math>\textstyle r=\sqrt{x^2+y^2}.</math> |
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Using the geometrical interpretation of [[sine]] and [[cosine]] and their periodicity in {{Math|2{{pi}}}}, any complex number {{mvar|z}} may be denoted as |
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: <math>z = x + iy = r (\cos \varphi + i \sin \varphi )= r (\cos (\varphi + 2k\pi) + i \sin (\varphi + 2k\pi)),</math> |
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for any integer number {{mvar|k}}. Evidently the argument of {{mvar|z}} is not uniquely specified: both {{mvar|φ}} and {{Math|1=''φ''' = ''φ'' + 2''k''{{pi}}}} are valid arguments of {{mvar|z}} for all integers {{mvar|k}}, because adding {{Math|2''k''{{pi}}}} [[Radian|radians]] or ''k''⋅360°{{refn|See [[radian]] for the conversion between 2[[pi|{{pi}}]] and 360 [[degree (angle)|degree]].|group=nb}} to {{mvar|φ}} corresponds to "winding" around the origin counter-clock-wise by {{mvar|k}} [[Turn (geometry)|turns]]. The resulting complex number is always {{mvar|z}}, as illustrated at the right for {{math|''k'' {{=}} 1}}. One may select exactly one of the possible arguments of {{mvar|z}} as the so-called ''principal argument'', denoted {{math|Arg(''z'')}}, with a capital {{math|A}}, by requiring {{mvar|φ}} to belong to one, conveniently selected turn, e.g. {{Math|−{{pi}} < ''φ'' ≤ {{pi}}}}<ref>{{Citation|last1=Ganguly|location=Kolkata|first1=S.|title=Elements of Complex Analysis|publisher=Academic Publishers|isbn=978-81-87504-86-3|year=2005}}, Definition 1.6.3</ref> or {{Math|0 ≤ ''φ'' < 2{{pi}}}}.<ref>{{Citation|last1=Nevanlinna|first1=Rolf Herman|author1-link=Rolf Nevanlinna|last2=Paatero|first2=Veikko|title=Introduction to complex analysis|journal=London: Hilger|location=Providence, RI|publisher=AMS Bookstore|isbn=978-0-8218-4399-4|year=2007|bibcode=1974aitc.book.....W}}, section 5.9</ref> These regions, where the argument of {{mvar|z}} is uniquely determined are called [[Principal branch|''branches'']] of the argument function. |
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[[Berkas:Complex_log_domain.svg|al=A density plot. In the middle there is a black point, at the negative axis the hue jumps sharply and evolves smoothly otherwise.|ka|jmpl|The principal branch (-{{pi}}, {{pi}}) of the complex logarithm, {{math|Log(''z'')}}. The black point at {{math|''z'' {{=}} 1}} corresponds to absolute value zero and brighter colors refer to bigger absolute values. The [[hue]] of the color encodes the argument of {{math|Log(''z'')}}.]] |
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[[Euler's formula]] connects the [[trigonometric functions]] [[sine]] and [[cosine]] to the [[complex exponential]]: |
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: <math>e^{i\varphi} = \cos \varphi + i\sin \varphi .</math> |
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Using this formula, and again the periodicity, the following identities hold:<ref>{{Citation|last1=Moore|first1=Theral Orvis|last2=Hadlock|first2=Edwin H.|title=Complex analysis|publisher=[[World Scientific]]|location=Singapore|isbn=978-981-02-0246-0|year=1991}}, section 1.2</ref> |
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: <math> \begin{array}{lll}z& = & r \left (\cos \varphi + i \sin \varphi\right) \\ |
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& = & r \left (\cos(\varphi + 2k\pi) + i \sin(\varphi + 2k\pi)\right) \\ |
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& = & r e^{i (\varphi + 2k\pi)} \\ |
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& = & e^{\ln(r)} e^{i (\varphi + 2k\pi)} \\ |
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& = & e^{\ln(r) + i(\varphi + 2k\pi)} = e^{a_k}, |
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\end{array} |
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</math> |
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where {{math|ln(''r'')}} is the unique real natural logarithm, {{math|''a''<sub>''k''</sub>}} denote the complex logarithms of {{mvar|z}}, and {{mvar|k}} is an arbitrary integer. Therefore, the complex logarithms of {{mvar|z}}, which are all those complex values {{math|''a''<sub>''k''</sub>}} for which the {{math|''a''<sub>''k''</sub>-th}} power of {{mvar|e}} equals {{mvar|z}}, are the infinitely many values |
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: <math>a_k = \ln (r) + i ( \varphi + 2 k \pi ),\quad</math> for arbitrary integers {{mvar|k}}. |
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Taking {{mvar|k}} such that {{Math|''φ'' + 2''k''{{pi}}}} is within the defined interval for the principal arguments, then {{math|''a''<sub>''k''</sub>}} is called the ''principal value'' of the logarithm, denoted {{math|Log(''z'')}}, again with a capital {{math|L}}. The principal argument of any positive real number {{mvar|x}} is 0; hence {{math|Log(''x'')}} is a real number and equals the real (natural) logarithm. However, the above formulas for logarithms of products and powers [[Exponentiation#Failure of power and logarithm identities|do ''not'' generalize]] to the principal value of the complex logarithm.<ref>{{Citation|last1=Wilde|first1=Ivan Francis|title=Lecture notes on complex analysis|publisher=Imperial College Press|location=London|isbn=978-1-86094-642-4|year=2006|url=https://books.google.com/books?id=vrWES2W6vG0C&q=complex+logarithm&pg=PA97}}, theorem 6.1.</ref> |
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The illustration at the right depicts {{math|Log(''z'')}}, confining the arguments of {{mvar|z}} to the interval {{open-closed|−π, π}}. This way the corresponding branch of the complex logarithm has discontinuities all along the negative real {{mvar|x}} axis, which can be seen in the jump in the hue there. This discontinuity arises from jumping to the other boundary in the same branch, when crossing a boundary, i.e. not changing to the corresponding {{mvar|k}}-value of the continuously neighboring branch. Such a locus is called a [[branch cut]]. Dropping the range restrictions on the argument makes the relations "argument of {{mvar|z}}", and consequently the "logarithm of {{mvar|z}}", [[Multi-valued function|multi-valued functions]]. |
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=== Inverses of other exponential functions === |
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Exponentiation occurs in many areas of mathematics and its inverse function is often referred to as the logarithm. For example, the [[logarithm of a matrix]] is the (multi-valued) inverse function of the [[matrix exponential]].<ref>{{Citation|last1=Higham|first1=Nicholas|author1-link=Nicholas Higham|title=Functions of Matrices. Theory and Computation|location=Philadelphia, PA|publisher=[[Society for Industrial and Applied Mathematics|SIAM]]|isbn=978-0-89871-646-7|year=2008}}, chapter 11.</ref> Another example is the [[P-adic logarithm function|''p''-adic logarithm]], the inverse function of the [[P-adic exponential function|''p''-adic exponential]]. Both are defined via Taylor series analogous to the real case.<ref>{{Neukirch ANT|mode=cs2}}, section II.5.</ref> In the context of [[differential geometry]], the [[Exponential map (Riemannian geometry)|exponential map]] maps the [[tangent space]] at a point of a [[Differentiable manifold|manifold]] to a [[Neighborhood (mathematics)|neighborhood]] of that point. Its inverse is also called the logarithmic (or log) map.<ref>{{Citation|last1=Hancock|first1=Edwin R.|last2=Martin|first2=Ralph R.|last3=Sabin|first3=Malcolm A.|title=Mathematics of Surfaces XIII: 13th IMA International Conference York, UK, September 7–9, 2009 Proceedings|url=https://books.google.com/books?id=0cqCy9x7V_QC&pg=PA379|publisher=Springer|year=2009|page=379|isbn=978-3-642-03595-1}}</ref> |
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In the context of [[finite groups]] exponentiation is given by repeatedly multiplying one group element {{mvar|b}} with itself. The [[discrete logarithm]] is the integer ''{{mvar|n}}'' solving the equation |
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: <math>b^n = x,</math> |
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where {{mvar|x}} is an element of the group. Carrying out the exponentiation can be done efficiently, but the discrete logarithm is believed to be very hard to calculate in some groups. This asymmetry has important applications in [[public key cryptography]], such as for example in the [[Diffie–Hellman key exchange]], a routine that allows secure exchanges of [[Cryptography|cryptographic]] keys over unsecured information channels.<ref>{{Citation|last1=Stinson|first1=Douglas Robert|title=Cryptography: Theory and Practice|publisher=[[CRC Press]]|location=London|edition=3rd|isbn=978-1-58488-508-5|year=2006}}</ref> [[Zech's logarithm]] is related to the discrete logarithm in the multiplicative group of non-zero elements of a [[finite field]].<ref>{{Citation|last1=Lidl|first1=Rudolf|last2=Niederreiter|first2=Harald|author2-link=Harald Niederreiter|title=Finite fields|publisher=Cambridge University Press|isbn=978-0-521-39231-0|year=1997|url-access=registration|url=https://archive.org/details/finitefields0000lidl_a8r3}}</ref> |
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{{anchor|double logarithm}}Further logarithm-like inverse functions include the ''double logarithm'' {{math|ln(ln(''x''))}}, the ''[[Super-logarithm|super- or hyper-4-logarithm]]'' (a slight variation of which is called [[iterated logarithm]] in computer science), the [[Lambert W function]], and the [[logit]]. They are the inverse functions of the [[double exponential function]], [[tetration]], of {{math|''f''(''w'') {{=}} ''we<sup>w</sup>''}},<ref>{{Citation|last1=Corless|year=1996|archive-date=14 December 2010|archive-url=https://web.archive.org/web/20101214110615/http://www.apmaths.uwo.ca/~djeffrey/Offprints/W-adv-cm.pdf|access-date=13 February 2011|s2cid=29028411|doi=10.1007/BF02124750|pages=329–59|volume=5|issn=1019-7168|journal=Advances in Computational Mathematics|url=http://www.apmaths.uwo.ca/~djeffrey/Offprints/W-adv-cm.pdf|first1=R.|title=On the Lambert ''W'' function|author5-link=Donald Knuth|first5=Donald|last5=Knuth|first4=D.|last4=Jeffrey|first3=D.|last3=Hare|first2=G.|last2=Gonnet|url-status=dead}}</ref> and of the [[logistic function]], respectively.<ref>{{Citation|last1=Cherkassky|first1=Vladimir|last2=Cherkassky|first2=Vladimir S.|last3=Mulier|first3=Filip|title=Learning from data: concepts, theory, and methods|publisher=[[John Wiley & Sons]]|location=New York|series=Wiley series on adaptive and learning systems for signal processing, communications, and control|isbn=978-0-471-68182-3|year=2007}}, p. 357</ref> |
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=== Related concepts === |
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From the perspective of [[group theory]], the identity {{math|log(''cd'') {{=}} log(''c'') + log(''d'')}} expresses a [[group isomorphism]] between positive [[Real number|reals]] under multiplication and reals under addition. Logarithmic functions are the only continuous isomorphisms between these groups.<ref>{{Citation|last1=Bourbaki|first1=Nicolas|author1-link=Nicolas Bourbaki|title=General topology. Chapters 5–10|publisher=[[Springer-Verlag]]|location=Berlin, New York|series=Elements of Mathematics|isbn=978-3-540-64563-4|mr=1726872|year=1998}}, section V.4.1</ref> By means of that isomorphism, the [[Haar measure]] ([[Lebesgue measure]]) {{math|''dx''}} on the reals corresponds to the Haar measure {{math|''dx''/''x''}} on the positive reals.<ref>{{Citation|last1=Ambartzumian|first1=R.V.|author-link=Rouben V. Ambartzumian|title=Factorization calculus and geometric probability|publisher=[[Cambridge University Press]]|isbn=978-0-521-34535-4|year=1990|url-access=registration|url=https://archive.org/details/factorizationcal0000amba}}, section 1.4</ref> The non-negative reals not only have a multiplication, but also have addition, and form a [[semiring]], called the [[probability semiring]]; this is in fact a [[semifield]]. The logarithm then takes multiplication to addition (log multiplication), and takes addition to log addition ([[LogSumExp]]), giving an [[isomorphism]] of semirings between the probability semiring and the [[log semiring]]. |
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[[Logarithmic form|Logarithmic one-forms ]]{{math|''df''/''f''}} appear in [[complex analysis]] and [[algebraic geometry]] as [[Differential form|differential forms]] with logarithmic [[Pole (complex analysis)|poles]].<ref>{{Citation|last1=Esnault|first1=Hélène|last2=Viehweg|first2=Eckart|title=Lectures on vanishing theorems|location=Basel, Boston|publisher=Birkhäuser Verlag|series=DMV Seminar|isbn=978-3-7643-2822-1|mr=1193913|year=1992|volume=20|doi=10.1007/978-3-0348-8600-0|citeseerx=10.1.1.178.3227}}, section 2</ref> |
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Themed skins and cosmetics from other games and properties have been added to ''Among Us'' as well: ''Innersloth'' and ''[[Riot Games]]'' crossed-over to bring ''[[Arcane (TV series)|Arcane]]'' themed cosmetics to ''Among Us''.<ref>{{Cite web|last=Zaidi|first=Taha|date=2021-11-12|title=Among Us x Arcane brings new League of Legends Cosmicube|url=https://www.upcomer.com/among-us-x-arcane-brings-new-league-of-legends-cosmicube/|website=Upcomer|language=en-US|archive-url=https://web.archive.org/web/20211112195925/https://www.upcomer.com/among-us-x-arcane-brings-new-league-of-legends-cosmicube/|archive-date=November 12, 2021|access-date=2021-11-14|url-status=live}}</ref> In addition to that Innersloth has also done crossovers with ''[[Halo (franchise)|Halo]]'',<ref>{{cite web|date=March 31, 2022|title=Among Us on Twitter|url=https://twitter.com/AmongUsGame/status/1509585338460622850|access-date=2022-04-03}}</ref> ''[[Ratchet & Clank]]'',<ref>{{cite web|date=March 31, 2022|title=Among Us on Twitter|url=https://twitter.com/AmongUsGame/status/1509584255038328833|access-date=2022-04-03}}</ref> and the movie franchise ''[[Scream (franchise)|Scream]]''.<ref>{{cite web|date=March 31, 2022|title=Among Us on Twitter|url=https://twitter.com/AmongUsGame/status/1509584089975644164|access-date=2022-04-03}}</ref> |
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The [[polylogarithm]] is the function defined by |
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Outside of the game itself ''Innersloth'' has collaborated with ''[[BT21]]'',<ref>{{cite web|date=November 23, 2021|title=BT21 on Twitter|url=https://twitter.com/BT21_/status/1462970465790853122|access-date=2022-04-03}}</ref> and Among Us-themed posters were used to advertise the movie ''[[Free Guy]]''.<ref>{{cite web|last=Griner|first=David|date=August 10, 2021|title=The Story Behind Free Guy's Pixel-Perfect Video Game Homage Posters|url=https://www.adweek.com/creativity/the-story-behind-free-guys-pixel-perfect-video-game-homage-posters/amp/|work=[[Adweek]]|access-date=2022-04-03}}</ref> The "ejected" animation was referenced in the season 2 trailer for the animated series ''[[Snoopy in Space]]'',<ref>{{cite web|date=October 19, 2021|title=Snoopy in Space: The Search for Life - Official Trailer (2021) Apple TV+|url=https://www.youtube.com/watch?v=kxjGi3aEaXw|access-date=2022-04-03}}</ref> and the Emergency Meeting screen was used in ''[[In Space with Markiplier]]''.<ref>{{cite web|date=March 18, 2022|title=Call an Emergency Meeting - In Space with Markiplier|url=https://www.youtube.com/watch?v=uoyvZ5mXiio|access-date=2022-04-12}}</ref> Among Us was also featured as a question on ''[[Jeopardy!]]''<ref>{{cite web|date=April 4, 2022|title=Kjerstin Iverson on Twitter|url=https://twitter.com/IversonKjerstin/status/1512185662811869187|access-date=2022-04-12}}</ref> |
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: <math> |
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\operatorname{Li}_s(z) = \sum_{k=1}^\infty {z^k \over k^s}. |
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</math> |
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[[Epic Games]] featured a community-created game mode in ''[[Fortnite Creative]]'' in December 2020 called "The Spy Within", which had very similar mechanics to ''Among Us'', in which among ten players, the others have to complete tasks to earn enough coins within a limited time while trying to deduce which two players are trying to sabotage that effort.<ref>{{cite web|last=Goslin|first=Austen|date=December 15, 2020|title=Fortnite's new limited time mode is basically Among Us|url=https://www.polygon.com/fortnite/2020/12/15/22176360/fortnite-new-limited-time-mode-among-us-impostor-spy-within|work=[[Polygon (website)|Polygon]]|access-date=August 18, 2021}}</ref> Epic later added another (official and internally-developed) limited mode to ''Fortnite'' called "Impostors" in August 2021, which was recognized as even a closer take on ''Among Us'', as the same basic mechanics as "The Spy Within" were used, but now taking place within an underground bunker with a layout similar to the ''Among Us'' map. Innersloth responded in frustration to this mode, which gave no credit to Innersloth. Innersloth's co-founder Marcus Bromander stated "Is it really that hard to put 10% more effort into putting your own spin on it though?", while studio representative Callum Underwood said that Innersloth was open to collaborations, "Just ask and if you follow some basic rules it’s usually fine".<ref>{{cite web|last=Good|first=Owen|date=August 18, 2021|title=Among Us developers push back on Fortnite's 'Impostors' mode|url=https://www.polygon.com/22630673/fortnite-impostors-among-us-ripoff-copyright-sue-patent|work=[[Polygon (website)|Polygon]]|access-date=August 18, 2021}}</ref> In an October 2021 blog posting, Epic Games did credit Innersloth and ''Among Us'' as inspirations for the "Impostors" mode.<ref>{{cite web|last=Phillips|first=Tom|date=October 12, 2021|title=Epic Games now credits Among Us' Innersloth as inspiration for Fortnite's Impostors mode|url=https://www.eurogamer.net/articles/2021-10-12-epic-games-now-credits-among-us-innersloth-as-inspiration-for-fortnites-imposters-mode|work=[[Eurogamer]]|access-date=October 12, 2021}}</ref> |
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It is related to the [[natural logarithm]] by {{math|1=Li<sub>1</sub> (''z'') = −ln(1 − ''z'')}}. Moreover, {{math|Li<sub>''s''</sub> (1)}} equals the [[Riemann zeta function]] {{math|ζ(''s'')}}.<ref>{{dlmf|id=25.12|first=T.M.|last=Apostol}}</ref> |
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== |
== Lihat pula == |
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{{Portal|Mathematics|Arithmetic|Chemistry|Geography|Engineering}} |
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* [[Dampak terhadap industri permainan video selama masa pandemik COVID-19]] |
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* [[Decimal exponent]] (dex) |
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* [[Exponential function]] |
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* [[Index of logarithm articles]] |
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* [[Logarithmic notation]] |
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== Notes == |
== Notes == |
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{{Notelist}} |
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{{reflist|30em|group=nb}} |
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== References == |
== References == |
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{{Reflist|refs=<ref name="itchpage">{{cite web |title=Among Us by Innersloth |url=https://innersloth.itch.io/among-us |website=itch.io |access-date=October 15, 2020 |language=en |archive-date=September 9, 2020 |archive-url=https://web.archive.org/web/20200909142044/https://innersloth.itch.io/among-us |url-status=live }}</ref> |
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{{Reflist}} |
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<ref name="outofbeta">{{Cite web|title=Among Us Out of Beta and Pricing – Among Us by Innersloth|url=https://innersloth.itch.io/among-us/devlog/55343/among-us-out-of-beta-and-pricing|last=Innersloth|website=[[Itch.io]]|date=November 8, 2018|access-date=September 27, 2020|language=en|archive-date=September 6, 2020|archive-url=https://web.archive.org/web/20200906012540/https://innersloth.itch.io/among-us/devlog/55343/among-us-out-of-beta-and-pricing|url-status=live}}</ref> |
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<ref name=":3">{{Cite web|last=Lugris|first=Mark|date=September 9, 2020|title=InnerSloth's Party Game Among Us Reaches 1.5 Million Simultaneous Players|url=https://www.thegamer.com/among-us-1-5-million-players-simultaneous-innersloth-party-game/|url-status=dead|archive-url=https://web.archive.org/web/20200921123233/https://www.thegamer.com/among-us-1-5-million-players-simultaneous-innersloth-party-game/|archive-date=September 21, 2020|access-date=September 9, 2020|website=TheGamer|language=en-US}}</ref> |
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<ref name=":6">{{Cite magazine|last=Matthews|first=Emma|date=September 15, 2020|title=Deceive your friends with these sneaky Among Us tips|url=https://www.pcgamer.com/among-us-imposter-crewmate-tips-guide-emergency-meeting/|url-status=live|archive-url=https://web.archive.org/web/20200921123245/https://www.pcgamer.com/among-us-imposter-crewmate-tips-guide-emergency-meeting/|archive-date=September 21, 2020|access-date=September 16, 2020|magazine=[[PC Gamer]]|language=en-US}}</ref> |
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<ref name=":1">{{Cite web|last=Pearson|first=Craig|date=August 27, 2020|title=Among Us has made a lying murderer out of me|url=https://www.rockpapershotgun.com/2020/08/27/among-us-has-made-lying-murderer-out-of-me/|url-status=dead|archive-url=https://web.archive.org/web/20200909025037/https://www.rockpapershotgun.com/2020/08/27/among-us-has-made-lying-murderer-out-of-me/|archive-date=September 9, 2020|access-date=September 8, 2020|website=[[Rock, Paper, Shotgun]]|language=en-US}}</ref> |
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<ref name=":2">{{Cite web|last=Lau|first=Evelyn|date=September 8, 2020|title='Among Us': what to know about the online survival game that's all about deceit|url=https://www.thenational.ae/arts-culture/among-us-what-to-know-about-the-online-survival-game-that-s-all-about-deceit-1.1074482|url-status=live|archive-url=https://web.archive.org/web/20200909024952/https://www.thenational.ae/arts-culture/among-us-what-to-know-about-the-online-survival-game-that-s-all-about-deceit-1.1074482|archive-date=September 9, 2020|access-date=September 8, 2020|website=[[The National (Abu Dhabi)|The National]]|language=en}}</ref> |
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<ref name=":5">{{Cite web|last=Penney|first=Andrew|date=September 16, 2020|title=Among Us Review: A Perfect Way To Ruin Your Friendships|url=https://www.thegamer.com/among-us-review/|url-status=live|archive-url=https://web.archive.org/web/20200921123255/https://www.thegamer.com/among-us-review/|archive-date=September 21, 2020|access-date=September 16, 2020|website=TheGamer|language=en-US}}</ref> |
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<ref name=":20">{{Cite web|last=Marshall|first=Cass|date=September 21, 2020|title=Among Us fans are calling everything 'pretty sus,' and it keeps working|url=https://www.polygon.com/2020/9/21/21449498/among-us-fans-pretty-sus-meme-explained|url-status=live|archive-url=https://web.archive.org/web/20200924153115/https://www.polygon.com/2020/9/21/21449498/among-us-fans-pretty-sus-meme-explained|archive-date=September 24, 2020|access-date=September 26, 2020|website=[[Polygon (website)|Polygon]]|language=en}}</ref> |
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<ref name=":0">{{Cite web|last=Marshall|first=Cass|date=September 11, 2020|title=Why Among Us' Emergency Meeting is the big social media mood|url=https://www.polygon.com/2020/9/11/21432684/among-us-emergency-meeting-meme-explained|access-date=September 13, 2020|website=[[Polygon (website)|Polygon]]|language=en|archive-date=September 21, 2020|archive-url=https://web.archive.org/web/20200921123243/https://www.polygon.com/2020/9/11/21432684/among-us-emergency-meeting-meme-explained|url-status=live}}</ref> |
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<ref name=":8">{{Cite web|last=Winslow|first=Jeremy|date=September 18, 2020|title=Among Us PS4, Xbox One Port More Complicated Than You Think|url=https://www.gamespot.com/articles/among-us-ps4-xbox-one-port-more-complicated-than-you-think/1100-6482373/|url-status=live|archive-url=https://web.archive.org/web/20200921123303/https://www.gamespot.com/articles/among-us-ps4-xbox-one-port-more-complicated-than-you-think/1100-6482373/|archive-date=September 21, 2020|access-date=September 19, 2020|website=[[GameSpot]]|language=en-US}}</ref> |
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<ref name=":9">{{Cite web|last=Paez|first=Danny|date=September 17, 2020|title='Among Us' dev offers disappointing update on progress for Xbox, PS4 ports|url=https://www.inverse.com/gaming/among-us-xbox-ps4-release-date-update|url-status=live|archive-url=https://web.archive.org/web/20200921123252/https://www.inverse.com/gaming/among-us-xbox-ps4-release-date-update|archive-date=September 21, 2020|access-date=September 19, 2020|website=[[Inverse (website)|Inverse]]|language=en}}</ref> |
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<ref name=":19">{{Cite web|last=Marshall|first=Cass|date=September 25, 2020|title=Among Us fans are creating their own crewsonas and sweet impostors|url=https://www.polygon.com/2020/9/25/21456451/among-us-fan-crew-sonas-impostor-culture-explained|url-status=live|archive-url=https://web.archive.org/web/20200926185819/https://www.polygon.com/2020/9/25/21456451/among-us-fan-crew-sonas-impostor-culture-explained|archive-date=September 26, 2020|access-date=September 27, 2020|website=[[Polygon (website)|Polygon]]|language=en}}</ref> |
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<ref name=":7">{{Cite web|last=Carless|first=Simon|date=September 10, 2020|title=Behind the dizzying ride to the top for Among Us|url=https://www.gamasutra.com/blogs/SimonCarless/20200910/369968/Behind_the_dizzying_ride_to_the_top_for_Among_Us.php|url-status=live|archive-url=https://web.archive.org/web/20200921123258/https://www.gamasutra.com/blogs/SimonCarless/20200910/369968/Behind_the_dizzying_ride_to_the_top_for_Among_Us.php|archive-date=September 21, 2020|access-date=September 16, 2020|website=[[Gamasutra]]|language=en}}</ref> |
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<ref name="gamerantsequel">{{Cite web|last=Brian|first=Renadette|date=August 19, 2020|title=Among Us 2 Announced Following First Game's Huge Surge In Popularity|url=https://gamerant.com/among-us-2-trailer/|url-status=live|archive-url=https://web.archive.org/web/20200909025037/https://gamerant.com/among-us-2-trailer/|archive-date=September 9, 2020|access-date=September 8, 2020|website=Game Rant|language=en-US}}</ref> |
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<ref name=":16">{{Cite magazine|last=Fenlon|first=Wes|date=September 24, 2020|title=How Among Us became so wildly popular|url=https://www.pcgamer.com/how-among-us-became-so-popular/|url-status=live|archive-url=https://web.archive.org/web/20200925235535/https://www.pcgamer.com/how-among-us-became-so-popular/|archive-date=September 25, 2020|access-date=September 25, 2020|magazine=[[PC Gamer]]|language=en-US}}</ref> |
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<ref name=":4">{{Cite web|last=Joseph|first=Funké|date=September 4, 2020|title=Why Among Us Became One of the Biggest Games on Twitch Two Years After Release|url=https://www.pastemagazine.com/games/among-us/among-us-game-twitch/|url-status=live|archive-url=https://web.archive.org/web/20200909025026/https://www.pastemagazine.com/games/among-us/among-us-game-twitch/|archive-date=September 9, 2020|access-date=September 8, 2020|website=[[Paste (magazine)|Paste]]|language=en}}</ref> |
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<ref name=":14">{{Cite web|last=Campbell|first=Amy|date=September 22, 2020|title=Among Us Devs Have Created a Gaming Phenomenon, Albeit Two Years After It Launched|url=https://www.escapistmagazine.com/v2/among-us-devs-have-created-a-gaming-phenomenon-albeit-two-years-after-it-launched/|url-status=live|archive-url=https://web.archive.org/web/20200924152953/https://www.escapistmagazine.com/v2/among-us-devs-have-created-a-gaming-phenomenon-albeit-two-years-after-it-launched/|archive-date=September 24, 2020|access-date=September 24, 2020|website=[[The Escapist (magazine)|Escapist Magazine]]|language=en-US}}</ref> |
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<ref name=":11">{{Cite web|last=Coto|first=Adrian|date=September 21, 2020|title=Among Us Surpasses PUBG With Almost 400,000 Concurrent Steam Players|url=https://screenrant.com/among-us-pubg-concurrent-players/|url-status=live|archive-url=https://web.archive.org/web/20200924153020/https://screenrant.com/among-us-pubg-concurrent-players/|archive-date=September 24, 2020|access-date=September 21, 2020|website=[[Screen Rant]]|language=en-US}}</ref> |
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<ref name="sequelannouncement">{{Cite web|author=Innersloth|date=August 18, 2020|title=Among Us 2 – Among Us by Innersloth|url=https://innersloth.itch.io/among-us/devlog/171026/among-us-2|url-status=dead|archive-url=https://web.archive.org/web/20200921123307/https://innersloth.itch.io/among-us/devlog/171026/among-us-2|archive-date=September 21, 2020|access-date=September 9, 2020|website=[[Itch.io]]|language=en}}</ref> |
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<ref name="techraptorsequel">{{Cite web|last=Perrault|first=Patrick|date=August 18, 2020|title=Among Us 2 Announced|url=https://techraptor.net/gaming/news/among-us-2-announced|url-status=live|archive-url=https://web.archive.org/web/20200909025029/https://techraptor.net/gaming/news/among-us-2-announced|archive-date=September 9, 2020|access-date=September 8, 2020|website=TechRaptor|language=en}}</ref> |
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<ref name="sequelsomag">{{Cite web|last=Manson|first=Leonard|date=September 4, 2020|title=Among Us 2 confirmed for PC and mobile; first details|url=https://www.somagnews.com/among-us-2-confirmed-for-pc-and-mobile-first-details/|url-status=dead|archive-url=https://web.archive.org/web/20200904223822/https://www.somagnews.com/among-us-2-confirmed-for-pc-and-mobile-first-details/|archive-date=September 4, 2020|access-date=September 8, 2020|website=Somag News|language=en-US}}</ref> |
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<ref name=":13"> |
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* {{Cite news|date=September 24, 2020|title=The game that's so popular, it can't have a sequel|language=en-GB|work=[[BBC News]]|url=https://www.bbc.com/news/newsbeat-54277123|access-date=September 24, 2020|archive-date=September 24, 2020|archive-url=https://web.archive.org/web/20200924152951/https://www.bbc.com/news/newsbeat-54277123|url-status=live |ref=none}} |
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* {{Cite web|last=Oloman|first=Jordan|title=Among Us 2 Cancelled, New Content Headed to Among Us 1|url=https://www.ign.com/articles/among-us-2-cancelled-among-us-1-updates|language=en|access-date=September 24, 2020|date=September 24, 2020|website=[[IGN]]|archive-date=September 24, 2020|archive-url=https://web.archive.org/web/20200924135125/https://www.ign.com/articles/among-us-2-cancelled-among-us-1-updates|url-status=live |ref=none}} |
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* {{Cite web|last=Carpenter|first=Nicole|date=September 24, 2020|title=Among Us 2 canceled — but don't worry|url=https://www.polygon.com/2020/9/24/21454185/among-us-2-canceled-innersloth-game|access-date=September 24, 2020|website=[[Polygon (website)|Polygon]]|language=en|archive-date=September 24, 2020|archive-url=https://web.archive.org/web/20200924153209/https://www.polygon.com/2020/9/24/21454185/among-us-2-canceled-innersloth-game|url-status=live |ref=none}} |
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* {{Cite web|last=Plunkett|first=Luke|date=September 23, 2020|title=Among Us 2 Cancelled One Month After It Was Announced|url=https://kotaku.com/among-us-2-cancelled-one-month-after-it-was-announced-1845160536|url-status=live|archive-url=https://web.archive.org/web/20200923234103/https://kotaku.com/among-us-2-cancelled-one-month-after-it-was-announced-1845160536|archive-date=September 23, 2020|access-date=September 24, 2020|website=[[Kotaku]]|language=en-us |ref=none}} |
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* {{Cite magazine|last=Prescott|first=Shaun|date=September 23, 2020|title=Among Us 2 cancelled in favour of ongoing work on the current game|url=https://www.pcgamer.com/among-us-2-cancelled-in-favour-of-ongoing-work-on-the-current-game/|access-date=September 24, 2020|magazine=[[PC Gamer]]|language=en-US|archive-date=September 24, 2020|archive-url=https://web.archive.org/web/20200924125705/https://www.pcgamer.com/among-us-2-cancelled-in-favour-of-ongoing-work-on-the-current-game/|url-status=live |ref=none}} |
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* {{Cite web|last=Peters|first=Jay|date=September 23, 2020|title=Among Us is so popular that its developers just canceled the sequel|url=https://www.theverge.com/2020/9/23/21453499/among-us-2-sequel-popular-canceled-developers-innersloth|access-date=September 24, 2020|website=[[The Verge]]|language=en|archive-date=September 24, 2020|archive-url=https://web.archive.org/web/20200924030235/https://www.theverge.com/2020/9/23/21453499/among-us-2-sequel-popular-canceled-developers-innersloth|url-status=live |ref=none}}</ref> |
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<ref name=":15">{{Cite web|last=Kent|first=Emma|date=September 24, 2020|title=Among Us 2 cancelled as devs focus on original title|url=https://www.eurogamer.net/articles/2020-09-24-among-us-2-cancelled-as-devs-focus-on-original-title|url-status=live|archive-url=https://web.archive.org/web/20200925235536/https://www.eurogamer.net/articles/2020-09-24-among-us-2-cancelled-as-devs-focus-on-original-title|archive-date=September 25, 2020|access-date=September 24, 2020|website=[[Eurogamer]]}}</ref> |
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<ref name=":10">{{Cite magazine|last=Matthews|first=Emma|date=August 25, 2020|title=Why Among Us is the best game to watch on Twitch right now|url=https://www.pcgamer.com/why-among-us-is-the-best-game-to-watch-on-twitch-right-now/|access-date=September 8, 2020|magazine=[[PC Gamer]]|language=en-US|archive-date=September 9, 2020|archive-url=https://web.archive.org/web/20200909025025/https://www.pcgamer.com/why-among-us-is-the-best-game-to-watch-on-twitch-right-now/|url-status=live}}</ref> |
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<ref name=":18">{{Cite web|last=Liao|first=Shannon|date=September 26, 2020|title=Among Us, a murder mystery set in space, is the latest multimillion dollar craze in video games|url=https://www.cnn.com/2020/09/26/tech/among-us-sequel-canceled/index.html|url-status=live|archive-url=https://web.archive.org/web/20200927064152/https://www.cnn.com/2020/09/26/tech/among-us-sequel-canceled/index.html|archive-date=September 27, 2020|access-date=September 27, 2020|website=[[CNN]]}}</ref> |
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<ref name="improb">{{Cite web|last=Grayson|first=Nathan|date=September 8, 2020|title=Among Us' Improbable Rise To The Top Of Twitch|url=https://www.kotaku.com.au/2020/09/among-us-improbable-rise-to-the-top-of-twitch/|url-status=dead|archive-url=https://web.archive.org/web/20200909025025/https://www.kotaku.com.au/2020/09/among-us-improbable-rise-to-the-top-of-twitch/|archive-date=September 9, 2020|access-date=September 8, 2020|website=[[Kotaku Australia]]|language=en-AU}}</ref> |
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<ref name=":17"> |
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* {{Cite web|last=Rothery|first=Jen|date=August 26, 2020|title=The best games like Among Us: seven of the top social deduction and imposter games|url=https://www.pcgamesn.com/social-deduction-games-like-among-us|url-status=live|archive-url=https://web.archive.org/web/20200921123303/https://www.pcgamesn.com/social-deduction-games-like-among-us|archive-date=September 21, 2020|access-date=September 14, 2020|website=[[PCGamesN]]|language=en-GB |ref=none}} |
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* {{cite web|last1=Marshall|first1=Cass|date=September 22, 2020|title=Among Us is much better without 'confirm eject'|url=https://www.polygon.com/2020/9/22/21450928/among-us-confirm-eject-setting-best-experience|url-status=live|archive-url=https://web.archive.org/web/20200924153020/https://www.polygon.com/2020/9/22/21450928/among-us-confirm-eject-setting-best-experience|archive-date=September 24, 2020|access-date=September 22, 2020|website=[[Polygon (website)|Polygon]] |ref=none}}</ref>}} |
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== External links == |
== External links == |
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* {{Commons category-inline}} |
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* {{Wiktionary-inline}} |
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*{{sister-inline|project=v|links=[[v:Speak Math Now!/Week 9: Six rules of Exponents/Logarithms|A lesson on logarithms can be found on Wikiversity]]|short=yes}} |
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* {{MathWorld|Logarithm|Logarithm|mode=cs2}} |
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* {{Official site}} |
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* [https://web.archive.org/web/20121218200616/http://www.khanacademy.org/math/algebra/logarithms-tutorial Khan Academy: Logarithms, free online micro lectures] |
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{{Portalbar|Video games|Science fiction|Internet|anime and manga}}{{Authority control}} |
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* {{springer|title=Logarithmic function|id=p/l060600}} |
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* {{Citation|author=Colin Byfleet|url=http://mediasite.oddl.fsu.edu/mediasite/Viewer/?peid=003298f9a02f468c8351c50488d6c479|title=Educational video on logarithms|access-date=12 October 2010}} |
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* {{Citation|author=Edward Wright|url=http://www.johnnapier.com/table_of_logarithms_001.htm|title=Translation of Napier's work on logarithms|access-date=12 October 2010|url-status=unfit|archive-url=https://web.archive.org/web/20021203005508/http://www.johnnapier.com/table_of_logarithms_001.htm|archive-date=3 December 2002}} |
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* {{Cite EB1911|wstitle=Logarithm|volume=16|pages=868–77|first=James Whitbread Lee|last=Glaisher|mode=cs2}} |
Revisi terkini sejak 2 Mei 2022 06.25
Among Us | |
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Gambar sampul | |
Versi pertama | |
Genre | |
Among Us[a] adalah sebuah permainan pemain jamak daring dan deduksi sosial tahun 2018 yang dikembangkan dan dipublikasikan oleh studio permainan asal Amerika Serikat, Innersloth. Permainan ini terinspirasi oleh sebuah permainan pesta Mafia dan film horor bertemakan fiksi ilmiah, The Thing. Video permainan ini tersedia untuk permainan lintas platform seperti perangkat iOS dan Android yang pertama kali dirilis pada Juni 2018 dan di Windows pada bulan November 2018. Kemudian video permainan ini diporta ke Nintendo Switch pada Desember 2020, dan di PlayStation 4, PlayStation 5, Xbox One dan Xbox Series X/S pada Desember 2021. Pada saat video permainan ini dirilis pada tahun 2018 dan menarik perhatiannya sedikit, permainan tersebut mendapatkan peningkatan popularitas yang sangat besar pada tahun 2020. Hal ini dikarenakan adanya banyak para streamer Twitch dan para YouTuber yang memainkannya. Sebuah permainan video versi VR yang dikembangkan oleh Schell Games, Among Us VR, akan dirilis untuk Quest 2, SteamVR, dan PlayStation VR.
Among Us mengambil latar tempat yang bertemakan luar angkasa, dimana para pemain terlihat seperti astronot berupa kartun, tanpa tangan, dan berwarna. Namun semenjak peta wahana antariksa "The Skeld" dirilis, tiga peta lainnya telah ditambahkan pada tahun sebelumnya seperti: menara puncak "MIRA HQ", pangkalan planet "Polus", dan "The Airship" (yang berasal dari serial Henry Stickmin, Infiltrating the Airship, juga dikembangkan oleh Innersloth). Masing-masing pemain memainkan salah satu dari dua peran (hampir semua yang diperankan adalah crewmate, namun ada jumlah sedikit pemain yang memerankan sebagai impostor) sehingga tidak dapat mengubah penampilannya.[b] Tujuan crewmate adalah mengidentifikasi dan melakukan pemungutan suara agar para Impostor dikeluarkan, atau menyelesaikan semua tugas-tugas di sekitar peta; sedangkan tujuan impostor adalh menyabotase misi para crewmate secara diam-diam dengan membunuh mereka sebelum mereka menyelesaikan tugasnya atau dengan memicu bencana yang tidak dapat mengatasinya.
Alur permainan
[sunting | sunting sumber]![A white-suited astronaut named "Buddy" (the player) stands in front of an unnamed blue-suited corpse. The room they are in is labeled "Admin". In the hallway, slightly obscured by the sight line mechanic, is a pink-suited astronaut named "Chum". In the upper-left corner of the player's screen, there is a fake list of tasks as well as the player's goal: to kill all Crewmates. The player also has the option to Use, Report, Sabotage, and Kill. As the player has just killed, the button is on cooldown and faded.](http://upload.wikimedia.org/wikipedia/id/thumb/4/4b/AmongUsWhiteKillBlue.png/282px-AmongUsWhiteKillBlue.png)
Among Us merupakan sebuah permainan video pemain jamak yang berjumlahkan empat hingga limabelas pemain (versi sebelumnya berjumlahkan empat hingga sepuluh pemain), meskipun jumlah minimumnya direkomendasi setidaknya lima pemain.[9] Pemain yang berjumlahkan tiga dipilih secara acak[10] dan secara diam-diam menjadi impostor pada setiap babak. Hingga pada tahun 2021, babak permainan dapat mengambil tempat pada salah satu dari empat peta: peta wahana antariksa yang disebut "The Skeld"; gedung kantor pusat yang disebut "MIRA HQ"; pangkalan planet yang disebut "Polus";[11] atau peta bertemakan pesawat luar angkasa yang disebut "The Airship" (yang berasal dari serial Innersloth, Henry Stickmin).[12][13]Pemain berperan sebagai impostor menang melalui salah satu dari dua cara berikut: dengan membunuh seluruh awak (hingga jumlahnya sama dengan jumlah impostor) atau dengan melakukan sabotase sistem kritikal pada peta (asalkan crewmate tidak mengatasinya dengan waktu yang tepat). Dengan demikian, para crewmate dapat memenangkan babak melalui salah satu dari dua cara berikut: dengan menyelesaikan semua tugas atau dengan mengidentifikasikan dan mengeluarkan semua impostor melalui pemungutan suara.[11] Permainan juga dapat diakhiri bila para pemain keluar dari babak jika dilakukan untuk memenuhi setiap kondisi agar menang (misalnya jika crewmate keluar dari permainan, maka tugas crewmate secara otomatis dianggap selesai).[14][15][16]
Pada saat permainan dimulai, crewmate diberi misi untuk menyelesaikan "tugas" (berupa minigame, minipuzzle, dan menekan tombol sederhana) di sekitar peta, meskipun hampir semua tugas memelihara sistem yang penting seperti memperbaiki kabel dan mengunduh data;[17] sedangkan impostor diberi daftar tugas palsu untuk berbaur dengan para crewmate. Akan tetapi, impostor tidak dapat mengerjakan tugas dan hanya dapat berpura-pura mengerjakan setiap tugas di dalam pesawat tersebut, serta impostor dapat menyabotase sistem penting (seperti pasokan oksigen di peta The Skeld), menutup pintu ruangan, berjalan diam-diam dan dengan cepat melalui sistem ventilasi, dan membunuh para crewmate ketika berdiri di dekatnya. Agar membantu para crewmate menemukan identitas impostor, ada beberapa sistem pengawasan pada masing-masing peta, seperti kamera keamanan dan sistem admin dalam peta The Skeld,[18] pintu masuk dengan banyaknya sensor dalam peta MIRA HQ,[19] dan indikator penting dalam peta Polus.[11] Para crewmate juga dapat mengkonfirmasi identitasnya melalui "tugas-tugas yang dapat dilihat" (seperti tugas yang mempunyai animasi ketika dimainkan pemain lain), sehingga para impostor tidak dapat memalsukannya.[20]Jika sebuah crewmate dibunuh atau setiap pemain dikeluarkan, maka mereka menjadi hantu. Hantu dapat melewati dinding, melihat aktivitas pemain lain, serta melihat dan mengirim pesan dengan hantu lainnya.[16] Pemain yang masih hidup mempunyai pandangan terbatas yang berbentuk kerucut,[21] sedangkan hantu tidak mempunyainya.[22] Terlebih lagi, para hantu tidak dapat berbicara dengan atau dilihat oleh pemain yang masih hidup. Para hantu (sebagai crewmate) membantu rekan-rekannya yang masih hidup dengan menyelesaikan tugasnya atau (sebagai impostor) melakukan berbagai tindakan berupa sabotase.[11]
Setiap pemain dapat memanggil pertemuan kelompok dengan melaporkan adanya mayat, atau dengan menekan tombol "pertemuan darurat" dalam peta kapan saja (kecuali saat terjadi sabotase di bagian utamanya, ketika "pertemuan darurat" tidak dapat dipanggil, namun masih bisa melaporkan adanya mayat).[16][23][24] Selama pertemuan berlangsung, pemain berdiskusi siapakah yang dipercayai berdasarkan bukti-bukti tersedia. Para impostor dapat diidentifikasi diluar dugaan bila mereka telah melakukan venting ataupun membunuh. Pemain dapat dicurigai karena ada banyak alasan lainnya. Namun, semua pemain membentuk semacam juri dan harus mempertimbangkan kejujuran ataupun nilai dari pernyataan setiap pemain lainnya dan bertanya saat melakukan pertemuan. Pemungutan suara dilakukan secara bersama, dan jika pemain memperoleh suara, maka yang mendapatkan pemungutan para crewmate terbanyak dikeluarkan dari peta dan menjadi hantu, kecuali sebagian besar para crewmate memilih untuk melewati pemungutan atau ketika pemungutannya seri.[17][16] Pemain dapat berkomunikasi melalui can obrolan teks (dengan ada beberapa frasa yang belum dijelaskan bagi pengguna ponsel),[17] namun hanya dilakukan saat pertemuan, dan hanya jika pemain hidup (walaupun hantu dapat berbicara dengan yang lain kapanpun).[11][16][21] Sementara bagi permainan yang tidak mempunyai sistem obrolan suara, pemain biasanya menggunakan program luar seperti Discord,[25][26][27] atau tetap sebaliknya jika para pemain tetap dekat dengan pemain yang lain. Jika para pemain mendengar suara setiap pemain lainnya, permainan tersebut mengingatkan mereka untuk tidak berbicara kecuali saat pertemuan.
Pada November 2021, ada beberapa peran tambahan yang tersedia bagi para pemain yang memperluas selain peran berupa Crewmate atau Impostor. Crewmate juga dapat menjadi Engineers (bahasa Indonesia: Ahli rekayasa), Scientists (bahasa Indonesia: Ilmuwan), atau Guardian Angels (bahasa Indonesia: Malaikat penjaga). Para engineer mengizinkan para crewmate untuk menjelajah melalui ventilasi seperti hal yang dapat dilakukan oleh impostor, albeit to a limited capacity. Scientists can check vitals at any time to see if any player has been killed recently. Crewmates who become Ghosts can become Guardian Angels, which can temporarily protect living players from being killed. Impostors likewise can be Shapeshifters, allowing them to temporarily morph into other players.In each game's lobby, various options can be adjusted to customize aspects of gameplay, such as player movement speed, the allowed number of emergency meetings, number of tasks, if there will be "visual tasks",[28] or whether or not an Impostor is revealed after being voted off.[29] There are also many cosmetic options, including spacesuit colors, skins, hats, and pets,[30][31] some of which are paid downloadable content.[c][33][5][21]
Pengembangan dan perilisan
[sunting | sunting sumber]Awal pengembangan
[sunting | sunting sumber]2018 | iOS/Android |
Windows | |
2019 | "MIRA HQ" |
"Polus" | |
2020 | Nintendo Switch |
2021 | "The Airship" |
PlayStation 4, PlayStation 5, Xbox One and Xbox Series X/S | |
2022 | |
2023 | |
TBA | Among Us VR |
Among Us terinspirasi oleh permainan pesta live Mafia,[33][34] dan film horror bertemakan fiksi ilmiah, The Thing.[35] Ide konsep permainan video ini berasal dari seorang pendiri Innersloth, Marcus Bromander, yang telah memainkan Mafia semenjak ia masih kanak-kanak. In the original game, function cards were dealt and players wandered around a house, aimlessly, while another person secretly killed the players, drawing a finger around their neck. Most of its mechanics were still present in Among Us, but the team wanted to "alleviate the need to create an interesting home model and have someone wandering around in a boring environment". So, they decided that the game would be space themed and also added tasks, which, according to Forest Willard, programmer at Innersloth, "changed several times during development".[35][36]
Pengembangan Among Us dimulai pada November 2017.[36] Permainan video ini pada awalnya bertujuan untuk menjadikannya sebuah permainan multipemain lokal dengan satu peta yang hanya dimainkan di ponsel .[37] Bromander menghentikan pengembangan permainan Innersloth lainnya, The Henry Stickmin Collection, yang bertujuan untuk membangun peta pertama permainan Among Us, The Skeld.[38] Ketika memulai pengembangan peta pertamanya, they intended that the ship was always in crisis and that the Impostors could do tasks. However, they found this setup "stressful" and decided that it "[wouldn't leave] much time for detective work and informed meeting conversations".[35][36] Willard described playtesting as painful and frustrating, as the game would break down during sessions forcing him to send playtesters new builds off of Google Play. The team tested the game with 8 of their friends and never tested the game with 9 or the maximum of 10 players.[38] The game was developed using the Unity engine.[39]
The game was released in June 2018 to Android and iOS under the AppID of "spacemafia".[33][40] Shortly after release, Among Us had an average player count of 30 to 50 concurrent players.[28] Bromander blamed the game's poor release on Innersloth being "really bad at marketing".[37] The team nearly abandoned the project multiple times, but continued work on it due to a "small but vocal player base",[41] adding in online multiplayer, new tasks, and customization options.[41] The game was released on Steam on November 16, 2018.[37][42] Cross-platform play was supported upon release of the Steam version.[43][44] Originally, the game had no audio to avoid revealing hidden information in a local setting,[d] and Willard mixed sounds from numerous sound packs to compose the SFX during the game's Steam release.[38]
On August 8, 2019, Innersloth released a second map, MIRA HQ,[45][46] a "tightly packed headquarters roughly the size of The Skeld." A third map, Polus, was added on November 12, 2019, and is set in a research station.[45][47] The fourth map, the Airship, was released on March 31, 2021, and is based on a location in the Henry Stickmin universe.[12][13] MIRA HQ and Polus originally cost players US$4 via in-app purchase. Their prices were reduced to US$2 on January 6, 2020, then made free on June 11, 2020.[48] While the map packs are still available for purchase on all platforms, they now only provide the player the skins that were bundled with the maps.[49] According to programmer Forest Willard, the team "stuck with [the game] a lot longer than we probably should have from a pure business standpoint", putting out regular updates to the game as often as once per week. This led to a steady increase in players, causing the game's player base to snowball. Bromander attributed this to the studio having enough savings to keep working on the game even while it was not selling particularly well.[37]
Sekuel yang dibatalkan dan pembaruan yang terus berlanjut
[sunting | sunting sumber]In August 2020, the team shifted focus onto a sequel, Among Us 2.[4][5][6][7] During this time, Forest Willard and Amy Liu continued to update Among Us, increasing the maximum player base, adding four servers and three regions,[50] and implementing longer multiplayer codes to support more concurrent games.[51] On September 23, 2020, the team canceled the sequel, instead opting to add all content intended for the sequel to the original Among Us, due to "how many people [were] enjoying [the original game]".[52][53][54] However, Innersloth deemed the game's codebase "outdated and not built to support adding so much new content", so the team made plans to rework the game's core code to enable adding new features.[54] The team subsequently announced their plans to fix the game's server issues and widespread cheating problem,[55][56][57] as well as add a system for banning disruptive players.[58] In October 2020, colorblind support for the "wires" task was added to the Among Us beta on Steam, as well as some previously unannounced lobby customization options.[59][60] As-of-yet unimplemented features include a fifth map, the Sheriff role, and new game modes.[52][53][58][61][62]
In mid-February 2021, the game added a feature called Quickchat, which replaces the standard chat interface with a series of preset phrases that players must pick from. Players under the age of 13 are required to use Quickchat, but those over 13 are also allowed to use Free Chat, which allows them to type original messages.[63][64] First announced at The Game Awards 2020, the Airship map was released on March 31, 2021.[12][13] The Airship features multiple floors, contraptions, tasks, and "more".[65][66] In addition, Game Awards presenter Geoff Keighley's face was added as a skin. The map itself is based upon the Henry Stickmin series's Toppat Clan Airship.[67] Innersloth also stated that the map would be free to all players.[68][13] It also features a skin bundle that includes Henry Stickmin-themed cosmetic that can be bought on Steam.[13]
The accounts system was implemented along with the update, and it allows players to report players that are not following Innersloth's Code of Conduct in order to make the game a welcoming and respectful place. Punishment ranges from temporary to a permanent ban. They also stated that reports would be viewed manually and not by bots, that account creations would be required if players want to use Free Chat or to customize their nicknames, and that people under the age of 13 would need their parents' permission to create an account. Implementing an account system also allowed Innersloth to add account linking and a friending system in future updates.[69][70] Innersloth later revealed on the game's official Twitter account a new color to the game, Rose, which was included in the game's next update along with five other colors: Coral, Tan, Gray, Maroon, and Banana, which were revealed during Summer Game Fest on June 10, 2021, alongside other upcoming content, including a fifth map, new Hide & Seek game mode, and new roles such as Sheriff and Scientist.[61][62] The new colors, along with 15 player lobby support, new meeting screen and revamp at the game's design, was released on June 15, 2021, during the game's 3rd anniversary.[9]
On July 7, 2021, Innersloth released a minor update that adds a new task, "Clean Vent", which involves the Crewmate cleaning a specific vent, preventing Impostors from using it.[71] On November 9, 2021, a major update was released that introduced four new roles, achievements, a level system, controller support, custom keybinds, visor cosmetics, cosmetic bundles called "Cosmicubes", various in-game currencies, and a major revamp to the in-game store.[72] On March 31, 2022, a friending system was added, which allows players to see who they recently played with, send and receive friend requests, send and receive lobby invites, as well as the ability to block people.[73]
During The Game Awards 2021, Among Us VR was announced for SteamVR, PlayStation VR, and the Meta Quest 2, developed by Schell Games.[74] During the Meta Quest Showcase on April 20, 2022, an aproximate release date was officially announced, with the game coming out around the holidays of 2022.[75]
Perilisan konsol
[sunting | sunting sumber]Amid its popularity, Innersloth considered releasing the game to PlayStation 4 and Xbox One consoles, but encountered a problem in implementing player communication, since standard text-based or voice-based chat seemed unusable. They considered a system similar to the "quick comms" system from Rocket League, as well as the possibility of developing an entirely new communication system for the game.[25][26] Versions of the game for Xbox consoles were later announced.[76]
Among Us was released for the Nintendo Switch on December 15, 2020, the same day it was announced during Nintendo Direct Indie World showcase. The Switch version supports cross-platform play with the mobile and Windows versions.[77] This port was published by Play EveryWare.[78] Upon release, the Switch version had an exploit to access The Airship prior to its official release in early 2021.[79] The exploit was fixed two days after release in the Switch version's first update.[80][81]
Among Us was released digitally for PlayStation 4, PlayStation 5, Xbox One and Xbox Series X/S consoles on December 14, 2021, along with its release on the Xbox Game Pass for console. These versions will support cross-platform play with existing Windows, Switch, and mobile versions. Unique to the PlayStation ports are special customization options based on Ratchet & Clank. Physical releases for consoles will be available in Europe the same day, while North American physical releases will be available in January 2022.[82]
Peretasan pada Oktober 2020 dan Januari 2021
[sunting | sunting sumber]Pada pertengahan Oktober 2020, seorang peretas bernama "Eris Loris" mulai menyerang sebagian besar server Amerika Utara. Ada beberapa pemain di subreddit dan Twitter Among Us melaporkan bahwa pemain ini meretas lobinya dan melakukan spam dalam obrolan permainan berupa promosi kanal YouTube-nya, pranala server Discord, dan pesan berupa politik yang bersifat kontroversial.[83] Eris Loris juga mengancam kepada pemain peretas secara pribadi bagi yang menolak untuk berlangganan dengan kanal YouTube-nya. Serber Discordnya yang telah ditemukan mengandung sejumlah unsur yang bersifat menyerang, seperti kata-kata rasis, mengandung unsur darah, pornografi dan gambar penyalahgunaan hewan.[84]
Laporan kanal Youtube bernama Eurogamer pada 23 Oktober 2020 menampilkan wawancara dengan seorang yang bernama Eris Loris. Wawancara tersebut diadakan melalui server Discord dari salah satu tautan yang tersedia dalam permainan yang diretas. Dalam wawancara, Loris mengklaim bahwa ia menciptakan bot yang bertanggunjawab atas peretasannya "hanya dalam enam jam", and had enlisted up to 50 volunteers to form a botnet which boosted the strength of their attacks. Loris mengklaim bahwa peretasan yang ia lakukan memberikan dampak terhadap 4,9 juta pemain dalam 1,5 juta permainan. Ia juga menambah bahwa peretasan tersebut merupakan bagian dari aksi publik yang bertujuan agar membujuk pemain untuk memilih Donald Trump sebagai presiden Amerika Serikat dalam pemilu tahun 2020.[84]
Innersloth menambahkan sebuah pesan dalam permainannya berupa peringatan kepada pemain mengenai peretasan yang terjadi pada 22 Oktober,[84] dan merilis sebuah pernyataan di Twitter pada keesokan harinya. Innersloth mengatakan bahwa mereka harus "sangat berhati-hati" terhadap masalah berupa peretasan, dan mengatakan bahwa "pembaruan server darurat" would be pushed out to combat the hacks. They encouraged players to stick to private games and to avoid playing on public ones until the update was released.[85] The team plans to address the hacking vulnerabilities as part of a planned overhaul for the game.[55][56][57] At the end of January 2021, players reported on Twitter the return of Eris Loris' hack attack, which is now distributing Among Us cheats.[86]
Popularitas
[sunting | sunting sumber]Naiknya popularitas pada tahun 2020
[sunting | sunting sumber]![Sodapoppin in a purple Twitch hoodie](http://upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Sodacrop.png/220px-Sodacrop.png)
While Among Us released in 2018, it was not until mid-2020 that it saw a surge of popularity, initially driven by content creators online in South Korea and Brazil. Bromander stated that the game is more popular in Mexico, Brazil, and South Korea than the United States.[37][33] According to Willard, Twitch streamer Sodapoppin first popularized the game on Twitch in July 2020.[37] Many other Twitch streamers and YouTubers followed suit, including prominent content creators xQc, Pokimane, Shroud, Ninja, Disguised Toast and PewDiePie.[53][87][34][88]
The COVID-19 pandemic was frequently cited as a reason for the popularity of Among Us, as it allowed for socializing despite social distancing.[37][89][90][91][92] Emma Kent of Eurogamer believed that the release of Innersloth's The Henry Stickmin Collection also contributed to awareness of Among Us,[53] and PC Gamer's Wes Fenlon credited Twitch streamer SR_Kaif for "prim[ing] Among Us for its big moment." Fenlon also praised Among Us for improvements over other popular tabletop games that had been inspired by Mafia, such as Secret Hitler. He said other video game adaptation of Mafia such as Town of Salem and Werewolves Within were "just add[ing] an online interface for the basic Werewolf rules," whereas Among Us is as an entirely new take on the concept.[34] Along with Fall Guys and the Jackbox Party Packs, Among Us provided a narrative-less experience that helped to avoid the "cultural trauma" of the pandemic, according to M.J. Lewis of Wired.[93]
Kumpulan meme dan fitur mod
[sunting | sunting sumber]Popularitas Among Us berlanjut pada beberapa bulan ke depan. YouTube melaporkan bahwa video tentang Among Us dilihat sebanyak 4 juta kali pada September 2020,[94] dan video TikTok yang mengandung topik Among Us dilihat sebanyak lebih dari 13 juta kali pada Oktober 2020.[95] YouTuber CG5 menulis sebuah lagu bernama"Show Yourself", yang diambil dari permainan Among Us pada September 2020, dan mendapat lebih dari 60 juta kali lihat dalam empat bulan.[96] [e] Pada September 2020, jumlah unduhan Among Us melebihi sebanyak 100 juta[34] dan jumlah pemain pada saat itu menaik hingga 1,5 juta pemain secara bersamaan[97][98][terj. kasar] (nearly 400 thousand of which were on Steam),[45] then peaked at 3.8 million in late September.[99] The sudden increase in players overloaded the game's server, which according to Willard was "a totally free Amazon server, and it was terrible." This forced him to work quickly, under crunch time, to resolve these issues.[41]
In August, Innersloth opened an online store for Among Us themed merchandise.[5][28] The game's popularity inspired many original songs, fanarts and internet memes,[18][23][41] Willard expressed that fan-created content "really is the best part" of making Among Us, and Bromander called it "my favorite thing to see".[41] The game popularized the slang word "sus" (meaning "suspicious" or "suspect"),[100][101][102] which had been used before the game's release.[103] Other slang terms as well as internet memes popularized and inspired by Among Us include 'Sussy' and 'Sussy Baka' (derived from "sus"),[104][105] 'When the Imposter is Sus' (an ironic meme based on Among Us, usually alongside an edited photo of Jerma985),[106] and 'Amogus' (satiric misspelling of "Among Us").[107][108]
During its time of widespread popularity, Among Us was controversially played by the U.S. Navy Esports team, in which players on the stream used in-game names referencing the N-word and the bombing of Nagasaki. The stream was deemed "offensive" and "intolerable" by some viewers.[109] In October 2020, U.S. Representatives Alexandria Ocasio-Cortez and Ilhan Omar streamed the game alongside several other prominent streamers such as Pokimane and Hasan Piker as a way to encourage people to vote in the 2020 United States presidential election, drawing almost 700,000 concurrent viewers on Twitch.[110][111][112]
Permainan video ini juga menerima beberapa mod yang dibuat oleh kounitas, seperti menambahkan peran baru, mode permainan, kosmetik, dsb.[113] Among Us juga ditampilkan di Twitch Rivals 2020, sebuah turnamen permainan daring yang diselenggarakan pada 4 Desember 2020.[114] Selama perayaan tersebut, pemain dapat menerima sebuah exclusive pet yang disebut "Glitch Pet", yang berupakan logo Twitch.[115]
Manga
[sunting | sunting sumber]Pada 28 Desember 2021, H2 Interactive, yang menerbitkan Among Us di Jepang, mengumumkan bahwa manga one-shot yang diambil dari permainan tersebut akan dipublikasikan dalam masalah April Bessatsu CoroCoro pada 28 Februari 2022.[116][117] Pada 13 Januari, Innersloth mulai mempromosikan manganya melalui akun Twitter resminya.[118]
Sambutan
[sunting | sunting sumber]Agregator | Skor |
---|---|
Metacritic | PC: 85/100[119] Switch: 79/100[120] |
Publikasi | Skor |
---|---|
4Players | 68/100[121] |
Game Informer | 8/10[122] |
IGN | 9/10[124] |
Jeuxvideo.com | 14/20[123] |
Nintendo Life | 8/10[125] |
PCMag | 4/5 (iOS)[126] |
Push Square | 7/10[127] |
Among Us was well received by critics. On the aggregator website Metacritic, the PC port received a 85 of 100 score based on 9 critic reviews, while the Nintendo Switch version received a 79 of 100 score based on 9 critic reviews, both them indicating "generally favorable reviews".[119][120] It was also considered one of the "Best PC Games for 2018", being ranked 17th, and as the "#38 Best Discussed PC Game of 2018".[128][129] Since December 2020, IGN considered it one of 2020's best reviewed games so far.[130]
Elliott Osange of Bonus Stage considered that the game is "silly fun", but felt that is more fun "to be an Impostor".[131] Craig Pearson of Rock, Paper, Shotgun had the same opinion, found playing as an Impostor "a lot more fun" than playing as a Crewmate, which he called "exhausting".[17] In reference to the game's popularity among streamers, Evelyn Lau of The National said: "Watching the reactions of people trying to guess who the impostor is (and sometimes getting it very wrong) or lying terribly about not being the impostor is all quite entertaining."[16] Alice O'Conner of Rock, Paper, Shotgun described the game as "Mafia or Werewolf but with minigames".[132] Andrew Penney of TheGamer said the game was "worth it for the price" and that "who you play with dictates how fun the game is."[21] L'avis de Tiraxa of Jeuxvideo.com praised the game's Freeplay mode, which offers newer players "to browse the map alone to accommodate the places", as they would need to play several games in order to "perfect their strategies".[123]
Leana Hafer from IGN stated in her verdict on the game: "I don't have any sus that this will be the last game of its breed to make a splash, since we’re already seeing its influence on even mega-games like Fortnite". As a negative point, she pointed out some technical problems, such as the difficulty of finding rooms that aren't already full or are a long way from getting there. She also lamented the lack of "mechanic to punish players who rage-quit when they don't get to play as impostor, or are caught dead to rights in the middle of a murder".[124] Tiraxa of Jeuxvideo.com was more critical of the game, lamenting the lack of an inbuilt voice chat, server bugs which "[prevent] some from joining the party, in a totally unexplained way", public servers with strangers, which she considered "less entertaining" than private servers with friends, and the large development progress, stating that the game has a "bit of a way to go before it reaches its full potential".[123] The mobile version of the game, although being free-to-play, was criticized. Osange of Bonus Stage called the presence of ads and in-app purchases of cosmetic changes that are mostly available for free on the PC version "nonsense". He also called the PC version "stable" but also stated that the Android version is "a device-by-device situation".[131]
The Nintendo Switch version received some criticism. William Antonelli of Insider said that the Switch controls give "many tasks a satisfying game response". However, he also stated that most of the tasks could be "done quickly with the Switch's touchscreen control", which can only be used when the console is in handheld mode. He noted that many of the game's tasks are difficult to complete using a gamepad, which is required when the console is connected to a larger screen, and considered this version "inferior" to the PC and mobile versions.[133] He also stated that the communication system is "frustrating", as using the joystick to select letters is "slow", and said the fact that the game has support for multiplayer across multiple platforms gives Switch players "immediate disadvantage".[133] PJ O'Reilly of Nintendo Life noted that the Switch lacked much of the additional content available on other platforms, such as skins, which he called a "shame".[125]
Among Us has been frequently compared to Fall Guys, as both became popular as party games during the COVID-19 pandemic;[37][27][134] the developers of both games have positively acknowledged each other on Twitter.[135][136] Comparisons have also been drawn between the two games' avatars, which have been said to look like jelly beans.[137][138] Among Us has also been compared to The Thing,[23][139] Town of Salem,[34][139] Werewolves Within,[34] and Secret Hitler.[34]
Sales
[sunting | sunting sumber]Hingga September 2020[update], Steam Spy estimated that the game had more than 10 million owners on Steam.[140] The Associated Press noted the game was the most downloaded app on the iOS App Store for both iPhones and iPads in October 2020.[141] According to SuperData Research, the game had roughly 500 million players worldwide hingga November 2020[update], with the free-to-play mobile version accounting for 97% of players and the buy-to-play PC version accounting for 3% of players, though it was the buy-to-play PC version that generated 64% of the game's gross revenue.[142] Among Us became one of the best selling games of 2020 on Steam, being listed on the platinum category on "The Year's Top 100" list.[143][144] The Nintendo Switch version's launch sold 3.2 million digital units in December 2020, making it the highest-earning version of the game for the month and one of the best-selling games on the Nintendo Switch.[145][146]
Pada Mei 2021, Among Us ditawarkan sebagai permainan gratis di Epic Games Store selama seminggu. Rata-rata pemain setiap hari melonjak dari sekitar 350.000 pemain dalam beberapa minggu sebelum mencapai lebih dari 2 juta pemain selama berlangsungnya giveaway.[147] Pada 29 Juni 2021, Innersloth melaporkan di Twitter bahwa setidaknya ada 15 juta salinan yang diklaim saat mempromisikan permainan gratis di Epic Games Store.[148]
Penghargaan
[sunting | sunting sumber]Penghargaan | Tanggal | Kategori | Hasil | Ref. |
---|---|---|---|---|
Golden Joystick 2020 | 24 November 2020 | style="background: #99FF99; color: black; vertical-align: middle; text-align: center; " class="yes table-yes2"|Menang | [149] | |
The Game Awards 2020 | 10 Desember 2020 | style="background: #99FF99; color: black; vertical-align: middle; text-align: center; " class="yes table-yes2"|Menang | [150][151] | |
style="background: #99FF99; color: black; vertical-align: middle; text-align: center; " class="yes table-yes2"|Menang | ||||
Steam Awards 2020 | 3 Januari 2021 | style="background: #FDD; color: black; vertical-align: middle; text-align: center; " class="no table-no2"|Nominasi | [152][153] | |
Nickelodeon Kids' Choice Awards | 13 Maret 2021 | style="background: #99FF99; color: black; vertical-align: middle; text-align: center; " class="yes table-yes2"|Menang | [154] |
Award | Date of ceremony | Category | Result | Ref. |
---|---|---|---|---|
Golden Joystick Awards 2020 | November 24, 2020 | style="background: #99FF99; color: black; vertical-align: middle; text-align: center; " class="yes table-yes2"|Menang | [155] | |
The Game Awards 2020 | December 10, 2020 | style="background: #99FF99; color: black; vertical-align: middle; text-align: center; " class="yes table-yes2"|Menang | [156][157] | |
style="background: #99FF99; color: black; vertical-align: middle; text-align: center; " class="yes table-yes2"|Menang | ||||
Steam Awards 2020 | January 3, 2021 | style="background: #FDD; color: black; vertical-align: middle; text-align: center; " class="no table-no2"|Nominasi | [158][159] | |
Nickelodeon Kids' Choice Awards | March 13, 2021 | style="background: #99FF99; color: black; vertical-align: middle; text-align: center; " class="yes table-yes2"|Menang | [160] | |
Webby Awards 2021 | May 18, 2021 | style="background: #99FF99; color: black; vertical-align: middle; text-align: center; " class="yes table-yes2"|Menang | [161][162] | |
Mobile Games Awards | July 20, 2021 | style="background: #99FF99; color: black; vertical-align: middle; text-align: center; " class="yes table-yes2"|Menang | [163][164] | |
International Game Developers Association | August 27, 2021 | style="background: #99FF99; color: black; vertical-align: middle; text-align: center; " class="yes table-yes2"|Menang | [165] | |
App Store Awards | December 2, 2021 | style="background: #99FF99; color: black; vertical-align: middle; text-align: center; " class="yes table-yes2"|Menang | [166] | |
British Academy Games Awards | April 7, 2022 | style="background: #FDD; color: black; vertical-align: middle; text-align: center; " class="no table-no2"|Nominasi | [167] |
Warisan
[sunting | sunting sumber]Among Us has done collaborations and cross-overs with other games and studios. The first game they collaborated with was Fall Guys, who added Among Us-themed skins to their game.[168] Characters from Among Us have made cameos in the indie games Astroneer,[169] Sunshine Heavy Industries,[170] Cosmonious High,[171] and Samurai Gunn 2,[172] and Among Us is referenced in several stickers in the game A Hat in Time.[173] Several Among Us-themed cards are included in The Binding of Isaac: Four Souls Requiem.[174]
Themed skins and cosmetics from other games and properties have been added to Among Us as well: Innersloth and Riot Games crossed-over to bring Arcane themed cosmetics to Among Us.[175] In addition to that Innersloth has also done crossovers with Halo,[176] Ratchet & Clank,[177] and the movie franchise Scream.[178]
Outside of the game itself Innersloth has collaborated with BT21,[179] and Among Us-themed posters were used to advertise the movie Free Guy.[180] The "ejected" animation was referenced in the season 2 trailer for the animated series Snoopy in Space,[181] and the Emergency Meeting screen was used in In Space with Markiplier.[182] Among Us was also featured as a question on Jeopardy![183]
Epic Games featured a community-created game mode in Fortnite Creative in December 2020 called "The Spy Within", which had very similar mechanics to Among Us, in which among ten players, the others have to complete tasks to earn enough coins within a limited time while trying to deduce which two players are trying to sabotage that effort.[184] Epic later added another (official and internally-developed) limited mode to Fortnite called "Impostors" in August 2021, which was recognized as even a closer take on Among Us, as the same basic mechanics as "The Spy Within" were used, but now taking place within an underground bunker with a layout similar to the Among Us map. Innersloth responded in frustration to this mode, which gave no credit to Innersloth. Innersloth's co-founder Marcus Bromander stated "Is it really that hard to put 10% more effort into putting your own spin on it though?", while studio representative Callum Underwood said that Innersloth was open to collaborations, "Just ask and if you follow some basic rules it’s usually fine".[185] In an October 2021 blog posting, Epic Games did credit Innersloth and Among Us as inspirations for the "Impostors" mode.[186]
Lihat pula
[sunting | sunting sumber]Notes
[sunting | sunting sumber]- ^ Saat membahas tentang sekuelnya yang direncanakan, permainan ini diberikan sebuah nama baru, yaitu Among Us 1, oleh pengembang permainan video beserta beberapa berita yang disalurkan.[4][5][6][7]
- ^ Permainan video ini menggunakan ejaan kata bahasa Inggris dalam "Impostor", bukan "Imposter" (meskipun kedua ejaan kata tersebut benar).[8]
- ^ Both the free mobile version of Among Us and the paid PC version have paid DLC. For the PC version, however, some of the mobile version's DLC is included in the standalone game.[32][33]
- ^ For example, the sound of an Impostor killing a Crewmate could reveal to other Crewmates who the Impostor was.
- ^ The song’s popularity led to 2 sequels, Lyin’ To Me and Good To Be Alive, released in November 2020 and February 2021, respectively.
References
[sunting | sunting sumber]- ^ "Among Us on Steam".
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- ^ a b Manson, Leonard (September 4, 2020). "Among Us 2 confirmed for PC and mobile; first details". Somag News (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal September 4, 2020. Diakses tanggal September 8, 2020.
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- ^ Garst, Aron. "Playing "Among Us?" Here are some tips and alternate rules to up the ante". The Washington Post (dalam bahasa Inggris). ISSN 0190-8286. Diakses tanggal October 9, 2020.
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- ^ Cuevas, Zackery (October 2, 2020). "All the differences between the PC and mobile versions of Among Us". Android Central. Diarsipkan dari versi asli tanggal October 13, 2020. Diakses tanggal October 2, 2020.
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- ^ Willard, Forest (September 10, 2020). "Servers Update (2020.9.9 beta) :: Among Us General Discussions". Steam Community (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal September 21, 2020. Diakses tanggal September 18, 2020.
- ^ a b
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- Oloman, Jordan (September 24, 2020). "Among Us 2 Cancelled, New Content Headed to Among Us 1". IGN (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal September 24, 2020. Diakses tanggal September 24, 2020.
- Carpenter, Nicole (September 24, 2020). "Among Us 2 canceled — but don't worry". Polygon (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal September 24, 2020. Diakses tanggal September 24, 2020.
- Plunkett, Luke (September 23, 2020). "Among Us 2 Cancelled One Month After It Was Announced". Kotaku (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal September 23, 2020. Diakses tanggal September 24, 2020.
- Prescott, Shaun (September 23, 2020). "Among Us 2 cancelled in favour of ongoing work on the current game". PC Gamer (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal September 24, 2020. Diakses tanggal September 24, 2020.
- Peters, Jay (September 23, 2020). "Among Us is so popular that its developers just canceled the sequel". The Verge (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal September 24, 2020. Diakses tanggal September 24, 2020.
- ^ a b c d Kent, Emma (September 24, 2020). "Among Us 2 cancelled as devs focus on original title". Eurogamer. Diarsipkan dari versi asli tanggal September 25, 2020. Diakses tanggal September 24, 2020.
- ^ a b Innersloth (September 23, 2020). "The Future of Among Us". Itch.io. Diarsipkan dari versi asli tanggal September 24, 2020. Diakses tanggal September 23, 2020.
- ^ a b Grayson, Nathan (October 2, 2020). "Among Us Has A Cheating Problem". Kotaku (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal October 3, 2020. Diakses tanggal October 4, 2020.
- ^ a b Marshall, Cass (October 8, 2020). "Among Us with randoms is rough". Polygon (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal October 9, 2020. Diakses tanggal October 9, 2020.
- ^ a b Wilde, Tyler (October 5, 2020). "Of course there are already Among Us cheaters". PC Gamer (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal October 9, 2020. Diakses tanggal October 9, 2020.
- ^ a b Turney, Alexandria (October 9, 2020). "Everything Among Us Desperately Needs To Add". Screen Rant (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal October 13, 2020. Diakses tanggal October 13, 2020.
- ^ Kent, Emma (October 12, 2020). "Among Us beta adds new ways to spice up investigations". Eurogamer (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal October 13, 2020. Diakses tanggal October 13, 2020.
- ^ Wheelock, Kyle (October 13, 2020). "Among Us Beta Updates Make Both Impostors' & Crewmates' Jobs Easier". Screen Rant (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal October 15, 2020. Diakses tanggal October 13, 2020.
- ^ a b Hetfeld, Malindy (May 21, 2021). "Among Us teases new crewmate colour ahead of 'next big update' announcement this June". PC Gamer. Diakses tanggal May 25, 2021.
- ^ a b J. Teuton, Christopher (June 10, 2021). "Among Us New Map & Hide and Seek Mode Revealed At Summer Games Fest". Screen Rant. Diakses tanggal June 14, 2021.
- ^ "What Among Us' New Quickchat Feature Is (& What It Does)". ScreenRant (dalam bahasa Inggris). 2021-03-08. Diakses tanggal 2021-04-25.
- ^ "Among Us introduces quick chat option that's "faster and safer"". Rock Paper Shotgun (dalam bahasa Inggris). 2021-03-08. Diakses tanggal 2021-04-25.
- ^ Team, M. G. H. (December 11, 2020). "Among Us 'The Airship' Map: Release Date, Leaks, Costumes and More". Mobile Gaming Hub (dalam bahasa Inggris). Diakses tanggal December 11, 2020.
- ^ Adler, Matthew (November 19, 2020). "Among Us Teases New Airship Map". IGN.
- ^ Skrebels, Joe (December 11, 2020). "Among Us Reveals New Map, The Airship". IGN Southeast Asia (dalam bahasa Inggris). Ziff Davis. Diakses tanggal December 14, 2020.
- ^ Innersloth (November 3, 2020). "Small Patch and Small Roadmap – Among Us by Innersloth". Itch.io. Diakses tanggal March 15, 2021.
- ^ Holt, Kris (March 24, 2021). "The upcoming 'Among Us' account system is mostly about making the game safer". Engadget. Diakses tanggal March 25, 2021.
- ^ Innersloth (March 24, 2021). "Info on Accounts – Among Us by Innersloth". Itch.io. Diakses tanggal March 25, 2021.
- ^ "Among Us July 7 Patch Notes: New Vent Cleaning Task, Bug Fixes". GameSpot (dalam bahasa Inggris). Diakses tanggal 2021-07-07.
- ^ Stanton, Rich (November 10, 2021). "Big Among Us update adds four new roles, an XP system, and multiple currencies". PC Gamer. Diakses tanggal November 20, 2021.
- ^ "Among Us on Twitter". March 31, 2022. Diakses tanggal April 21, 2022.
- ^ Valentine, Rebekah (December 9, 2021). "Among Us Vents Into VR". IGN.
- ^ "Holiday 2022. Happy, purple?". Twitter. April 20, 2022. Diakses tanggal April 21, 2022.
- ^ "Here's everything you need to know about Among Us for Xbox". Windows Central. 2021-02-06. Diakses tanggal 2021-04-20.
- ^ Farokhmanesh, Megan (December 15, 2020). "Among Us launches for the Nintendo Switch today". The Verge (dalam bahasa Inggris). Diakses tanggal December 15, 2020.
- ^ Innersloth (March 18, 2021). "📣 March 31 – The Airship Releases! – Among Us by Innersloth". Itch.io. Diakses tanggal March 20, 2021.
- ^ Lee, Julia (December 16, 2020). "How to play Among Us' new Airship map on Nintendo Switch". Polygon (dalam bahasa Inggris). Diakses tanggal December 23, 2020.
- ^ rawmeatcowboy (December 20, 2020). "Among Us Airship map glitch fixed". gonintendo.com (dalam bahasa Inggris). Diakses tanggal December 23, 2020.
- ^ "List of Nintendo Switch game patches/updates". benoitren.be (dalam bahasa Inggris). December 21, 2020. Diarsipkan dari versi asli tanggal December 23, 2020. Diakses tanggal December 23, 2020.
- ^ Warren, Tom (October 21, 2021). "Among Us is coming to Xbox, PlayStation, and Xbox Game Pass on December 14th". The Verge. Diakses tanggal October 21, 2021.
- ^ Mukherjee, Arnab (October 24, 2020). "Among Us Hacker: Who is Eris Loris & how to respond to his Among Us hack /spam attack – guide". The SportsRush (dalam bahasa Inggris). Diakses tanggal October 25, 2020.
- ^ a b c Emma, Kent (October 23, 2020). "Among Us is dealing with a huge spam attack". Eurogamer (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal October 24, 2020. Diakses tanggal October 24, 2020.
- ^ Innersloth (October 23, 2020). "Innersloth's Response to the hacking problem". Twitter (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal October 24, 2020. Diakses tanggal October 24, 2020.
- ^ Khan, Aqdas (January 30, 2021). "Eris Loris Among Us : "Another hack wave?", Players ask questions as Eris Loris hack is reportedly back". The Sports Rush (dalam bahasa Inggris). Diakses tanggal February 7, 2021.
- ^ Zheng, Jenny (September 21, 2020). "Among Us Is Even More Popular Than You Think Right Now". GameSpot (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal September 23, 2020. Diakses tanggal September 24, 2020.
- ^ "Disguised Toast Talks More About Not Being Invited to Jimmy Fallon Among Us Game". Game Rant (dalam bahasa Inggris). 2021-12-08. Diakses tanggal 2022-01-04.
- ^ "What is 'Among Us', and How Did It Get So Popular? – Review Geek". www.reviewgeek.com (dalam bahasa Inggris). Diakses tanggal April 7, 2021.
- ^ Epstein, Adam. "How an obscure 2018 computer game became a global phenomenon overnight". Quartz (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal October 2, 2020. Diakses tanggal October 2, 2020.
- ^ Stuart, Keith (September 29, 2020). "Among Us is the ultimate party game of the Covid era". The Guardian (dalam bahasa Inggris). Diakses tanggal October 2, 2020.
- ^ Sands, Sean (August 23, 2020). "'Among Us' Is Not Just the Game of 2020, It's '2020: The Game'". Vice (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal October 1, 2020. Diakses tanggal October 2, 2020.
- ^ Lewis, M.J. (December 4, 2020). "Among Us and a Resurgence of Narrative-Free Games". Wired. Diakses tanggal December 4, 2020.
- ^ ""Among Us" Surged in September – "Among Us" videos topped 4 billion views in September", YouTube Culture and Trends, October 14, 2020, diarsipkan dari versi asli tanggal October 15, 2020, diakses tanggal October 14, 2020,
Among Us is an online multiplayer social deduction game developed by an American indie game studio, Innersloth. Among Us is a space-themed game in which a crew of astronauts must complete tasks while trying to figure out who among them is an imposter, who is sabotaging their work and killing the other players. The game has been available for about two years, but viewership of videos related to the game soared last month. There were over 4 billion views of videos related to Among Us in September.
- ^ Lorenz, Taylor (October 14, 2020), "With Nowhere to Go, Teens Flock to Among Us – YouTubers, influencers and streamers popularized the multiplayer game. Then their fans started playing too.", The New York Times, diarsipkan dari versi asli tanggal October 14, 2020, diakses tanggal October 14, 2020,
When an indie game company created Among Us in 2018, it was greeted with little fanfare. The multiplayer game remained under the radar as many games do — until the summer of the pandemic. Eager to keep viewers entertained during quarantine, Chance Morris, known online as Sodapoppin, began streaming the game, created by InnerSloth, to his 2.8 million followers on Twitch in July. By mid-September, Among Us caught on like wildfire. Suddenly major YouTube stars, TikTok influencers, and streamers were playing it. PewDiePie, James Charles, and Dr. Lupo have all played the game for millions.
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- ^ Lugris, Mark (September 9, 2020). "InnerSloth's Party Game Among Us Reaches 1.5 Million Simultaneous Players". TheGamer (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal September 21, 2020. Diakses tanggal September 9, 2020.
- ^ * Macgregor, Jody (September 9, 2020). "Multiplayer space mystery Among Us hits 1.5 million simultaneous players". PC Gamer (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal September 21, 2020. Diakses tanggal September 12, 2020.
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- Zheng, Jenny (September 18, 2020). "Among Us Is Really, Really Popular Right Now". GameSpot (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal September 21, 2020. Diakses tanggal September 19, 2020.
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- ^ Rodriguez, Salvador (October 14, 2020), "How Amazon's Twitch turned an obscure game called Among Us into a pandemic mega-hit", CNBC, diarsipkan dari versi asli tanggal October 15, 2020, diakses tanggal October 14, 2020,
Developed by InnerSloth, a small studio in Redmond, Washington, Among Us was download nearly 42 million times on Steam in the first half of September, according to Safebettingsites.com, and it was downloaded nearly 84 million times on iOS and Android that month, according to SensorTower. The game hasn’t left the top five on Apple’s U.S. App Store since Sept. 1, and it has seen more than 158 million installs worldwide across the App Store and Google Play to date, SensorTower says.
- ^ Marshall, Cass (September 21, 2020). "Among Us fans are calling everything 'pretty sus,' and it keeps working". Polygon (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal September 24, 2020. Diakses tanggal October 15, 2020.
- ^ Kim, Alina (October 5, 2020). "Red Is Lowkey Sus: A Political Reflection on "Among Us"". The Chicago Maroon (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal October 15, 2020. Diakses tanggal October 15, 2020.
- ^ "Sus | Definition of Sus by Oxford Dictionary on Lexico.com also meaning of Sus". Lexico Dictionaries | English (dalam bahasa Inggris). Diakses tanggal October 19, 2020.
- ^ "What is "Sussy Baka" on TikTok? Among Us & anime trend goes viral". Dexerto (dalam bahasa Inggris). 5 May 2021. Diakses tanggal 1 April 2022.
- ^ Ainswroth, Harry (5 April 2021). "What does 'sussy baka' mean and why does everyone on TikTok say it?". The Tab. Diakses tanggal 1 August 2021.
- ^ "When The Imposter Is Sus/Sus Jerma". Know Your Meme. Diarsipkan dari versi asli tanggal December 5, 2020.
- ^ "Fellow fans of legumes, take a gander at these official Among Us costumes". Nintendo Wire. 16 September 2021. Diakses tanggal 17 September 2021.
- ^ "Random: 'Amogus' Is A Playable Among Us Pokémon Hack". Nintendo Life. 4 March 2021. Diakses tanggal 17 September 2021.
- ^ * Lemon, Jacon (September 13, 2020). "US Navy's Twitch account criticized for streaming games with offensive player names". Newsweek (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal September 21, 2020. Diakses tanggal September 15, 2020.
- Gault, Matthew (September 14, 2020). "A U.S. Navy Twitch Stream Included Jokes About Nagasaki and the N-Word". Vice (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal September 21, 2020. Diakses tanggal September 15, 2020.
- Grayson, Nathan (September 15, 2020). "Navy Twitch Stream Spirals Out Of Control Due To Slur, War Crime Jokes". Kotaku Australia (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal September 21, 2020. Diakses tanggal September 17, 2020.
- Marchetto, Claudia (September 14, 2020). "Among Us: la Marina americana lo gioca su Twitch usando nickname razzisti ed è bufera". Eurogamer.it (dalam bahasa Italia). Diarsipkan dari versi asli tanggal September 21, 2020. Diakses tanggal September 15, 2020.
- ^ Brown, Abram (October 20, 2020). "Almost 700,000 People Flock To Twitch To Watch Alexandria Ocasio-Cortez Play Hit Video Game 'Among Us'". Forbes (dalam bahasa Inggris). Diakses tanggal October 21, 2020.
- ^ Ziady, Hanna (October 21, 2020). "Alexandria Ocasio-Cortez just played a video game on Twitch to encourage voting". CNN. Diakses tanggal October 21, 2020.
- ^ "Alexandria Ocasio-Cortez Streams On Twitch With Hasan Piker And Pokimane, Draws Over 430,000 Viewers". Kotaku (dalam bahasa Inggris). Diakses tanggal October 21, 2020.
- ^ Matheus, Emma (March 22, 2021). "The best Among Us mods to try with your friends". PC Gamer. Diakses tanggal March 25, 2021.
- ^ Mukherjee, Arnab (December 6, 2020). "Twitch Rivals Among Us Showdown: Trainwrecks wins for the 4th time in a row, Glitch Pet Twitch Drops active on his channel!". The Sports Rush. Diakses tanggal March 25, 2021.
- ^ Sayles, Lauren (December 9, 2020). "How to get the free Twitch Glitch pet to use in Among Us". PC Invasion. Diakses tanggal March 25, 2021.
- ^ Morrissy, Kim (January 14, 2022). "Among Us Video Game Gets 1-Shot Manga In February". Anime News Network. Diakses tanggal January 15, 2022.
- ^ H2 INTERACTIVE公式アカウント [@H2InteractiveJP] (December 28, 2021). "Among Usの読み切り漫画が別冊コロコロ4月号に登場します!お楽しみに⭐️" (Tweet) (dalam bahasa Jepang). Diakses tanggal January 15, 2022 – via Twitter.
- ^ Innersloth [@InnerslothDevs] (January 12, 2022). "Surpriseeeee! @AmongUsGame will have a 1 shot manga feature in Bessatsu Corocoro magazine on April 2022 Sparkles" (Tweet) (dalam bahasa Jepang). Diakses tanggal January 15, 2022 – via Twitter.
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- ^ a b "Among Us (Switch)". Metacritic. Fandom, Inc. Diakses tanggal February 14, 2021.
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- ^ a b Hafer, Leana (December 22, 2020). "Among Us Review". IGN.
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- ^ "Best PC Games for 2018". Metacritic. Diakses tanggal March 25, 2021.
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- ^ a b Osange, Elliott (September 23, 2020). "Among Us Review". Bonus Stage. Diakses tanggal March 15, 2021.
- ^ O'Conner, Alice (September 8, 2020). "Among Us had 1.5 million people playing at the same time this weekend". Rock Paper Shotgun. Diarsipkan dari versi asli tanggal September 9, 2020. Diakses tanggal September 8, 2020.
- ^ a b Antonelli, William (December 23, 2020). "'Among Us' is the biggest game of 2020, but don't play it on the Nintendo Switch". Insider. Diakses tanggal February 17, 2021.
- ^ Liao, Shannon (September 26, 2020). "Among Us, a murder mystery set in space, is the latest multimillion dollar craze in video games". CNN. Diarsipkan dari versi asli tanggal September 27, 2020. Diakses tanggal September 27, 2020.
- ^ Fall Guys [@FallGuysGame] (September 23, 2020). "This is actually true
We love Among Us 😍" (Tweet) – via Twitter. - ^ Forest Willard [@forte_bass] (September 23, 2020). "This is horrifying.
I love it" (Tweet) – via Twitter. - ^ Fairfax, Zackerie (September 27, 2020). "A Fall Guys X Among Us Crossover Could Happen (& It Just Makes Sense)". Screen Rant (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal October 8, 2020. Diakses tanggal October 4, 2020.
- ^ Harris, Iain (October 1, 2020). "Someone has modded Among Us's Red into Left 4 Dead 2, naturally". PCGamesN (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal October 3, 2020. Diakses tanggal October 4, 2020.
- ^ a b
- Rothery, Jen (August 26, 2020). "The best games like Among Us: seven of the top social deduction and imposter games". PCGamesN (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal September 21, 2020. Diakses tanggal September 14, 2020.
- Marshall, Cass (September 22, 2020). "Among Us is much better without 'confirm eject'". Polygon. Diarsipkan dari versi asli tanggal September 24, 2020. Diakses tanggal September 22, 2020.
- ^ Peters, Jay (September 23, 2020). "Among Us is so popular that its developers just canceled the sequel". The Verge. Diakses tanggal February 20, 2021.
- ^ "The top iPhone and iPad apps on Apple App Store", The Washington Post, Associated Press, October 13, 2020, diarsipkan dari versi asli tanggal October 15, 2020, diakses tanggal October 13, 2020,
1. Among Us!, InnerSloth LLC
- ^ "November 2020 worldwide digital games market". SuperData Research. Nielsen Company. December 18, 2020. Diarsipkan dari versi asli tanggal December 18, 2020. Diakses tanggal December 19, 2020.
- ^ Blake, Vikki (December 28, 2020). "Steam reveals 2020's most-played and best-selling PC games". GamesRadar+. Diakses tanggal January 1, 2021.
- ^ Vincent, Brittany (December 26, 2020). "Cyberpunk 2077, Among Us Top Steam's Best-Selling Games of 2020". PCMag. Diakses tanggal January 1, 2021.
- ^ "Worldwide digital games market: December 2020". SuperData Research. Nielsen Company. January 22, 2021. Diarsipkan dari versi asli tanggal January 22, 2021. Diakses tanggal January 22, 2021.
- ^ Pastro, Max (January 25, 2021). "Among Us Nintendo Switch Version Sold Over 3 Million Units". Screen Rant. Diakses tanggal March 15, 2021.
- ^ Bailey, Dustin (May 31, 2021). "Among Us goes from 350k daily PC players to two million after Epic giveaway". PCGamesN. Diakses tanggal May 31, 2021.
- ^ "Among Us Downloaded on Epic Games Store 15 Million Times During Giveaway". ScreenRant (dalam bahasa Inggris). 2021-07-01. Diakses tanggal 2021-07-01.
- ^ Tyrer, Ben (November 24, 2020). "Among Us developer wins this year's Breakthrough Award at the Golden Joysticks". GamesRadar+. Diarsipkan dari versi asli tanggal November 28, 2020. Diakses tanggal November 28, 2020.
- ^ Makuch, Eddie (November 18, 2020). "New Among Us Map Teased, Announcement Coming At The Game Awards". GameSpot. Diarsipkan dari versi asli tanggal November 19, 2020. Diakses tanggal November 19, 2020.
- ^ Ryan, Jackson (December 10, 2020). "The Game Awards 2020: Every result, winner, world premiere, trailers and more". CNET (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal December 11, 2020. Diakses tanggal December 11, 2020.
- ^ Izaak (December 20, 2020). "Steam Awards 2020 nominees revealed". Sportskeeda. Diakses tanggal November 19, 2020.
- ^ "The Steam Awards". Steam. January 3, 2021. Diarsipkan dari versi asli tanggal January 24, 2021. Diakses tanggal January 27, 2021.
- ^ Liz Calvario (March 13, 2021). "2021 Kids' Choice Awards: The Complete Winners List". Entertainment Tonight. Diakses tanggal March 13, 2021.
- ^ Tyrer, Ben (November 24, 2020). "Among Us developer wins this year's Breakthrough Award at the Golden Joysticks". GamesRadar+. Diarsipkan dari versi asli tanggal November 28, 2020. Diakses tanggal November 28, 2020.
- ^ Makuch, Eddie (November 18, 2020). "New Among Us Map Teased, Announcement Coming At The Game Awards". GameSpot. Diarsipkan dari versi asli tanggal November 19, 2020. Diakses tanggal November 19, 2020.
- ^ Ryan, Jackson (December 10, 2020). "The Game Awards 2020: Every result, winner, world premiere, trailers and more". CNET (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal December 11, 2020. Diakses tanggal December 11, 2020.
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- ^ "The Steam Awards". Steam. January 3, 2021. Diarsipkan dari versi asli tanggal January 24, 2021. Diakses tanggal January 27, 2021.
- ^ Liz Calvario (March 13, 2021). "2021 Kids' Choice Awards: The Complete Winners List". Entertainment Tonight. Diakses tanggal March 13, 2021.
- ^ "Among Us". The Webby Awards (dalam bahasa Inggris). Diakses tanggal 2021-06-15.
- ^ "WINNERS ANNOUNCED FOR THE 25TH ANNUAL WEBBY AWARDS | The Webby Awards". The Webby Awards (dalam bahasa Inggris). Diakses tanggal 2021-10-25.
- ^ "Mobile Games Awards on Twitter" (dalam bahasa Inggris). Diakses tanggal 2022-04-03.
- ^ "The Winners of 2021 - Mobile Games Awards" (dalam bahasa Inggris).
- ^ "International Game Developers Association (IGDA)". International Game Developers Association (dalam bahasa Inggris). August 27, 2021. Diakses tanggal 2022-04-03.
- ^ "Announcing the App Store Award Winners - The 15 best apps and games of 2021" (dalam bahasa Inggris). December 2, 2021. Diakses tanggal 2022-04-03.
- ^ "BAFTA 2022". British Academy Games Awards (dalam bahasa Inggris). Diakses tanggal 2022-04-03.
- ^ Parrish, Ash (June 30, 2021). "Fall Guys' Latest Costume Is Very Suspicious". Kotaku. Diakses tanggal August 18, 2021.
- ^ "ASTRONEER on Twitter". July 29, 2021. Diakses tanggal 2022-04-03.
- ^ "Version 1.1.3 - Among Us crossover mission; dirty engine rebalance". October 8, 2021. Diakses tanggal 2022-04-03.
- ^ "Among Us Crewmate Enters 3D World Of Cosmonious High In New Collab". GameSpot. March 25, 2022. Diakses tanggal 2022-04-04.
- ^ "Samurai Gunn 2 × Among Us update is now live!". December 16, 2021. Diakses tanggal 2022-04-03.
- ^ "A Hat in Time on Twitter". March 4, 2022. Diakses tanggal 2022-04-03.
- ^ "Among Us Invades Binding Of Isaac: Four Souls With Crossover Cards". Screen Rant. June 24, 2021. Diakses tanggal 2022-04-03.
- ^ Zaidi, Taha (2021-11-12). "Among Us x Arcane brings new League of Legends Cosmicube". Upcomer (dalam bahasa Inggris). Diarsipkan dari versi asli tanggal November 12, 2021. Diakses tanggal 2021-11-14.
- ^ "Among Us on Twitter". March 31, 2022. Diakses tanggal 2022-04-03.
- ^ "Among Us on Twitter". March 31, 2022. Diakses tanggal 2022-04-03.
- ^ "Among Us on Twitter". March 31, 2022. Diakses tanggal 2022-04-03.
- ^ "BT21 on Twitter". November 23, 2021. Diakses tanggal 2022-04-03.
- ^ Griner, David (August 10, 2021). "The Story Behind Free Guy's Pixel-Perfect Video Game Homage Posters". Adweek. Diakses tanggal 2022-04-03.
- ^ "Snoopy in Space: The Search for Life - Official Trailer (2021) Apple TV+". October 19, 2021. Diakses tanggal 2022-04-03.
- ^ "Call an Emergency Meeting - In Space with Markiplier". March 18, 2022. Diakses tanggal 2022-04-12.
- ^ "Kjerstin Iverson on Twitter". April 4, 2022. Diakses tanggal 2022-04-12.
- ^ Goslin, Austen (December 15, 2020). "Fortnite's new limited time mode is basically Among Us". Polygon. Diakses tanggal August 18, 2021.
- ^ Good, Owen (August 18, 2021). "Among Us developers push back on Fortnite's 'Impostors' mode". Polygon. Diakses tanggal August 18, 2021.
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External links
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