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yang dilihat dari mengambil persamaan pendefinisian <math> x = b^{\,\log_b x} = b^y</math> ke kuasa (pangkat) <math>\tfrac{1}{y}.</math>
==ParticularBasis baseskhusus==
[[FileBerkas:Log4.svg|thumb|upright=1.2|PlotsPlot oflogaritma logarithmuntuk for basesbasis 0.,5, 2, anddan {{mvar|e}}]]
AmongDi allantara choicessemua forpilihan theuntuk basebasis, threeketiganya areadalah particularlybasis commonkhusus. TheseIni areadalah {{math|1=''b'' = 10}}, {{math|1=''b'' = [[e (mathematicalkonstanta constantmatematika)|''e'']]}} (the [[IrrationalBilangan numberirasional|irrationalirasional]] mathematicaladalah constantkonstanta matematika ≈ 2.,71828), anddan {{math|1=''b'' = 2}} (the [[binarylogaritma logarithmbiner]]). InDalam [[mathematicalanalisa analysismatematika]], the logarithmbasis baselogaritma {{mvar|e}} istersebar widespreadluas becausekarena ofsifat analyticalanalitik propertiesyang explaineddijelaskan belowdibawah ini. OnDi the othersisi handlain, logaritma {{nowrap|basebasis-10}} logarithms are easymudah todigunakan useuntuk forperhitungan manual calculationsdalam insistem thebilangan [[decimaldesimal]] number system:<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}}, chapterbab 17, phal. 275</ref>
:<math>\log_{10}(10 x) = \log_{10} 10 + \log_{10} x = 1 + \log_{10} x.\ </math>
ThusJadi, {{math|log<sub>10</sub>  (''x'')}} isberhubungan relateddengan to the number ofjumlah [[decimaldigit digitdesimal]]s ofdari abilangan positivebulat integerpositif {{mvar|x}}: thejumlah number of digits is thedigit smallestadalah [[integerbilangan bulat]] strictlyterkecil yang lebih biggerbesar thandari {{math|1=log<sub>10</sub> (''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}}, phal. 20</ref> For exampleMisalnya, {{math|log<sub>10</sub>(1430)}} isadalah approximatelykira-kira 3.,15. TheBilangan nextbulat integerberikutnya isadalah 4, whichyang ismerupakan thejumlah number of digits ofdigit 1430. BothBaik thelogaritma naturalalami logarithmdan andlogaritma theke logarithmbasis todua basedigunakan two are used indalam [[informationteori theoryinformasi]], correspondingsesuai todengan the use ofpenggunaan [[nat (unitsatuan)|nat]]s oratau [[bit]]s assebagai thesatuan fundamentaldasar unitsinformasi of information, respectivelymasing-masing.<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> BinaryLogaritma logarithmsbiner arejuga alsodigunakan used indalam [[computerilmu sciencekomputer]], where thedimana [[binarysistem numeralbilangan systembiner|binarysistem systembiner]] isada ubiquitousdi mana-mana; indalam [[musicteori theorymusik]], wheredi amana pitchrasio rationada of twodua (the [[octaveoktaf]]) isada ubiquitousdi andmana-mana thedan [[centsen (musicmusik)|centsen]] isadalah thelogaritma binary logarithmbiner (scaled byskala 1200) ofrasio theantara ratiodua betweennada twoyang adjacentbertemperatur equally-temperedsama pitches in Europeandi [[classicalmusik musicklasik]] Eropa; anddan indalam [[photographyfotografi]] tountuk measuremengukur [[exposurenilai valueeksposur]]s.<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>
TheTabel followingberikut tablemencantumkan listsnotasi commonumum notationsuntuk forlogaritma logarithmske tobasis theseini basesdan and the fields wheremedan theydimana aremereka useddigunakan. ManyBanyak disciplinesdisiplin writemenulis {{math|log log ''x''}} insteadyang ofdialihkan ke {{math|log<sub>''b''</sub>  ''x''}}, whenketika thedasar intendedyang basedimaksud canditentukan bedari determined from the contextkonteksnya. The notationNotasi {{math|<sup>''b''</sup>log log ''x''}} alsojuga occursmuncul.<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 MarchMaret 2011 |language=de}}</ref> TheKolom "notasi ISO notation" column listsmencantumkan designationspenunjukan suggestedyang bydisarankan theoleh [[InternationalOrganisasi OrganizationInternasional foruntuk StandardizationStandardisasi]] ([[ISO 80000-2]]).<ref>QuantitiesKuantitas anddan unitssatuan – PartBagian 2: MathematicsMatematika (ISO 80000-2:2019); EN ISO 80000-2</ref> Because theKarena notationnotasi {{math|log {{mvar|x}}}} hastelah beendigunakan useduntuk forketiga all three basesbasis (oratau whenjika thebasisnya basetidak istentu indeterminateatau ortidak immaterialmaterial), thedasar intendedyang basedimaksud mustseringkali oftenharus bedisimpulkan inferredberdasarkan basedkonteks onatau context or disciplinedisiplin. InDalam computerilmu sciencekomputer, {{Math|log}} usuallybiasanya refersmengacu topada {{math|log<sub>2</sub>}}, anddan indalam mathematicsmatematika {{Math|log}} usuallybiasanya refersmengacu topada {{math|log<sub>''e''</sub>}}.<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=OneSalah ofsatu theaspek interestingyang andmenarik sometimesdan eventerkadang surprisingmengejutkan aspectsdari ofanalisis the analysis ofstruktur data structuresdan andalgoritma algorithmsadalah iskeberadaan thelogaritma ubiquitousdi presencemana-mana of logarithms ... AsSeperti iskebiasaan thedalam customliteratur in the computing literaturekomputasi, wekami omitmenghilangkan writingpenulisan the basebasis {{mvar|b}} ofdari thelogaritma logarithm whenketika {{math|1=''b'' = 2}}.}}</ref> InDalam otherkonteks contextslain, {{Math|log}} oftensering disebut meanssebagai {{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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