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==HistorySejarah==
{{Main|HistorySejarah of logarithmslogaritma}}
The '''historySejarah of logarithms'logaritma'' indimulai seventeenth-centurydari EuropeEropa isabad theketujuh discoverybelas of aadalah newpenemuan [[functionfungsi (mathematicsmatematika)|functionfungsi]] thatbaru extendedyang thememperluas realmranah ofanalisis analysisluar beyondcakupan themetode scope of algebraic methodsaljabar. TheMetode methodlogaritma ofdikemukakan logarithms was publiclysecara propoundedterbuka byoleh [[John Napier]] inpada tahun 1614, indalam asebuah bookbuku titledberjudul ''Mirifici Logarithmorum Canonis Descriptio'' (''DescriptionDeskripsi ofKaidah theLogaritma Wonderfulyang Rule of LogarithmsMenakjubkan'').<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> PriorSebelum topenemuan Napier's invention, thereada hadteknik beenlain otherdengan techniquescakupan of similar scopesserupa, such as theseperti [[prosthaphaeresisprosthafaeresis]] oratau thepenggunaan usetabel ofprogresi, tablesyang ofdikembangkan progressions,secara extensivelyekstensif developed byoleh [[Jost Bürgi]] aroundsekitar 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 coinedmenciptakan theistilah termuntuk forlogaritma logarithmdalam in Middlebahasa Latin, “logarithmusTengah,” derived“logaritmus” fromyang theberasal Greekdari bahasa Yunani, literallysecara harfiah meaningberarti, “ratio“rasio-numberbilangan,” fromdari ''logos'' “proportion“proporsi, ratiorasio, word”kata” + ''arithmos'' “number”“bilangan”.
The [[commonLogaritma logarithmumum]] ofsuatu abilangan numberadalah isindeks thepangkat index of that power ofsepuluh tenyang whichsama equalsdengan thebilangan numbertersebut.<ref>William Gardner (1742) ''Tables of Logarithms''</ref> SpeakingBerbicara oftentang aangka numberyang asmembutuhkan requiringbanyak soangka manyadalah figureskiasan iskasar auntuk roughlogaritma allusion to common logarithmumum, anddan wasdisebut referred to byoleh [[Archimedes]] as the “order ofsebagai a“urutan number”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> The firstLogaritma real logarithmspertama wereadalah heuristicmetode methodsheuristik tountuk turnmengubah multiplicationperkalian intomenjadi additionpenjumlahan, thussehingga facilitatingmemudahkan rapidkomputasi computationyang cepat. SomeBeberapa ofmetode theseini methodsmenggunakan usedtabel tablesyang derivedditurunkan fromdari trigonometricidentitas identitiestrigonometri.<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> SuchMetode methodsseperti areitu calleddisebut [[prosthaphaeresisprosthafaeresis]].
Invention of the [[function (mathematics)|function]] now known as the [[natural logarithm]] began as an attempt to perform a [[quadrature (mathematics)|quadrature]] of a rectangular [[hyperbola]] by [[Grégoire de Saint-Vincent]], a Belgian Jesuit residing in Prague. Archimedes had written ''[[The Quadrature of the Parabola]]'' in the third century BC, but a quadrature for the hyperbola eluded all efforts until Saint-Vincent published his results in 1647. The relation that the logarithm provides between a [[geometric progression]] in its [[argument of a function|argument]] and an [[arithmetic progression]] of values, prompted [[A. A. de Sarasa]] to make the connection of Saint-Vincent's quadrature and the tradition of logarithms in [[prosthaphaeresis]], leading to the term “hyperbolic logarithm”, a synonym for natural logarithm. Soon the new function was appreciated by [[Christiaan Huygens]], and [[James Gregory (mathematician)|James Gregory]]. The notation Log y was adopted by [[Gottfried Wilhelm Leibniz|Leibniz]] in 1675,<ref>[[Florian Cajori]] (1913) "History of the exponential and logarithm concepts", [[American Mathematical Monthly]] 20: 5, 35, 75, 107, 148, 173, 205.</ref> and the next year he connected it to the [[integral calculus|integral]] <math display="inline">\int \frac{dy}{y} .</math>
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