[[Berkas:PDF-log_normal_distributions.svg|al=ThreeTiga asymmetrickurva PDFfungsi kepadatan probabilitas yang curvesasimetrik|ka|jmpl|ThreeTiga [[Probabilityfungsi densitykepadatan function|probability density functionsprobabilitas]] (PDF) ofdari randomvariabel variablesacak withdengan sebaran log-normal distributions. TheParameter locationlokasi parameter {{math|μ}},whichyang isbernilai zeronol foruntuk allsemua threetiga offungsi the PDFs showntersebut, ismerupakan thepurata meanlogaritma ofdari thevariabel logarithm of the random variableacak, not the meanbukan ofpurata thedari variablevariabel itselftersendiri.]]
[[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|DistributionSebaran ofdigit first digitspertama (indalam bentuk %persentase, reddengan bars)batang inberwarna themerah) dalam [[ListDaftar ofnegara countriesmenurut byjumlah populationpenduduk|populationjumlah ofpopulasi thedari 237 countriesnegara]] ofdi the worlddunia. BlackTitik dotsberwarna indicatehitam themenunjukkan distributionsebaran predictedyang bydiprediksi Benford'smenurut lawhukum Benford.]]
Logarithms arise inDalam [[probabilityteori theoryprobabilitas]]: the, [[lawhukum ofbilangan large numbersbesar]] dictatesmengatakan thatbahwa, foruntuk asebuah [[fairmata coinuang seimbang]], asketika thejumlah numberpelemparan ofkoin coin-tossesnaik increasesmenuju to infinitytakhingga, themaka observedkesebandingan proportiondari ofgambar headskepala (atau ekor) yang diamati [[BinomialSebaran distributionbinomial|approachesmendekati satu one-halfsetengah]]. TheFluktuasi fluctuationsdari ofnilai thiskesebandingan proportionyang aboutbernilai one-halfsatu aresetengah describeddijelaskan bymelalui thehukum [[lawyang ofmenggunakan thelogaritma, yaitu [[hukum iteratedlogaritma logarithmteriterasi]].<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>
LogarithmsLogaritma alsojuga occurmuncul indalam [[LogSebaran log-normal|sebaran distribution|log-normal distributions]]. When the logarithmKetika oflogaritma adari [[randomvariabel variableacak]] has amempunyai [[sebaran normal distribution]], themaka variablevariabel isdikatakan saidmempunyai to have asebaran 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> LogSebaran log-normal distributionsditemukan aredalam encounteredbanyak in many fieldsbidang, <u>wherever</u> asebuah variablevariabel isdibentuk formedsebagai ashasilkali thedari productbanyaknya ofvariabel manyacak independentindenpenden positivebernilai random variables, for examplepositif. inContohnya theseperti studydalam ofmempelajari turbulenceturbulensi.<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>
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>
