noun · 2 senses · updated from the 2026-07-25 local source snapshot
Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.
Sound
Pronunciation
Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.
UK:/ˈlɒɡ.ə.ɹɪ.ð(ə)m/
UK:/ˈlɔɡ.ə.ɹɪ.ð(ə)m/
Southern-England:Recorded audio is listed in the source snapshot.
US:/ˈlɑ.ɡə.ɹɪ.ð(ə)m/
US:/ˈlɑ.ɡəɹ.ɹɪ.ðəm/
US:/ˈlɑɡ.ə.ɹɪðm/
US:/ˈlɑɡ.əɹ.ɹɪðm/
Canada:/ˈlɑ.ɡə.ɹɪ.ð(ə)m/
CMU ARPABET:L AA1 G ER0 IH2 DH AH0 M
Digits mark lexical stress: 1 primary, 2 secondary, 0 unstressed.
1
noun
Meaning 1
For a number x, the exponent by which a given base number must be raised in order to obtain the power x. Written log _bx. For example, log 101000=3 because 103=1000 and log 216=4 because 24=16.
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, sciences
Examples
For a currency which uses denominations of 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, etc., each jump in the base-10 logarithm from one denomination to the next higher is either 0.3010 or 0.3979.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
2
noun
Meaning 2
the exponent required to produce a given number
Definition source: Princeton WordNet 3.0
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: log
Antonyms: none provided
Broader terms: exponent, power, index
Narrower terms: common logarithm, natural logarithm, Napierian logarithm
History
Etymology
From New Latin logarithmus, coined by Scottish mathematician John Napier from Ancient Greek λόγος (lógos, “ratio, proportion”) and ἀριθμός (arithmós, “number”). Napier set a geometric progression (a sequence of equal ratios) against an arithmetic progression (a sequence of equal differences), so that the logarithm of a number counts the ratios separating it from a starting value, turning multiplication into addition.
Across languages
Translations
65 source translations are retained for this English entry.
Arabic:
أَسِيس
(ʔasīs)
— The power to which a given base number must be raised in order to obtain a given number
Arabic:
لُوغَارِثْم
(lūḡāriṯm)
— The power to which a given base number must be raised in order to obtain a given number
Armenian:
լոգարիթմ
(logaritʻm)
— The power to which a given base number must be raised in order to obtain a given number
Bulgarian:
логаритъм
(logaritǎm)
— The power to which a given base number must be raised in order to obtain a given number
Burmese:
လော့ဂရစ်သမ်
(lau.ga.racsam)
— The power to which a given base number must be raised in order to obtain a given number
Catalan:
logaritme
— The power to which a given base number must be raised in order to obtain a given number
Chinese:
對數 /对数
(zh-min-nan)
— The power to which a given base number must be raised in order to obtain a given number
Chinese Mandarin:
對數 /对数
(duìshù)
— The power to which a given base number must be raised in order to obtain a given number
Czech:
logaritmus
— The power to which a given base number must be raised in order to obtain a given number
Danish:
logaritme
— The power to which a given base number must be raised in order to obtain a given number
Dutch:
logaritme
— The power to which a given base number must be raised in order to obtain a given number
Esperanto:
logaritmo
— The power to which a given base number must be raised in order to obtain a given number
Finnish:
logaritmi
— The power to which a given base number must be raised in order to obtain a given number
French:
logarithme
— The power to which a given base number must be raised in order to obtain a given number
Galician:
logaritmo
— The power to which a given base number must be raised in order to obtain a given number
Georgian:
ლოგარითმი
(logaritmi)
— The power to which a given base number must be raised in order to obtain a given number
German:
Logarithmus
— The power to which a given base number must be raised in order to obtain a given number
Greek:
λογάριθμος
(logárithmos)
— The power to which a given base number must be raised in order to obtain a given number
Gujarati:
લઘુગણક
(laghugṇak)
— The power to which a given base number must be raised in order to obtain a given number
Hawaiian:
huhui helu
— The power to which a given base number must be raised in order to obtain a given number
Hindi:
लघुगणक
(laghugṇak)
— The power to which a given base number must be raised in order to obtain a given number
Hungarian:
logaritmus
— The power to which a given base number must be raised in order to obtain a given number
Icelandic:
logri
— The power to which a given base number must be raised in order to obtain a given number
Indonesian:
logaritma
— The power to which a given base number must be raised in order to obtain a given number
Italian:
logaritmo
— The power to which a given base number must be raised in order to obtain a given number
Japanese:
対数
(taisū)
— The power to which a given base number must be raised in order to obtain a given number
Kannada:
ಪೆರ್ಚುಪಟ್ಟು
(percupaṭṭu)
— The power to which a given base number must be raised in order to obtain a given number
Kannada:
ಪಟ್ಟೇರುಕ
(paṭṭēruka)
— The power to which a given base number must be raised in order to obtain a given number
Kannada:
ಲಘುಗಣಕ
(laghugaṇaka)
— The power to which a given base number must be raised in order to obtain a given number
Khmer:
លោការីត
(lookaariit)
— The power to which a given base number must be raised in order to obtain a given number
Korean:
로그
(rogeu)
— The power to which a given base number must be raised in order to obtain a given number
Korean:
대수
(daesu)
— The power to which a given base number must be raised in order to obtain a given number
Latin:
logarithmus
— The power to which a given base number must be raised in order to obtain a given number
Latvian:
logaritms
— The power to which a given base number must be raised in order to obtain a given number
Macedonian:
логари́там
(logarítam)
— The power to which a given base number must be raised in order to obtain a given number
Māori:
taupū kōaro
— The power to which a given base number must be raised in order to obtain a given number
Māori:
pūkōaro
— The power to which a given base number must be raised in order to obtain a given number
Norwegian Bokmål:
logaritme
— The power to which a given base number must be raised in order to obtain a given number
Norwegian Nynorsk:
logaritme
— The power to which a given base number must be raised in order to obtain a given number
Polish:
logarytm
— The power to which a given base number must be raised in order to obtain a given number
Portuguese:
logaritmo
— The power to which a given base number must be raised in order to obtain a given number
Punjabi:
ਲਘੂਗਣਕ
(laghūgṇak)
— The power to which a given base number must be raised in order to obtain a given number
Romanian:
logaritm
— The power to which a given base number must be raised in order to obtain a given number
Russian:
логари́фм
(logarífm)
— The power to which a given base number must be raised in order to obtain a given number
Serbo-Croatian:
логаритам
— The power to which a given base number must be raised in order to obtain a given number
Serbo-Croatian:
logaritam
— The power to which a given base number must be raised in order to obtain a given number
Shona:
mhetapawa
— The power to which a given base number must be raised in order to obtain a given number
Shona:
davanharu
— The power to which a given base number must be raised in order to obtain a given number
Sinhalese:
ලඝු ගණක
(laghu gaṇaka)
— The power to which a given base number must be raised in order to obtain a given number
Slovene:
logaritem
— The power to which a given base number must be raised in order to obtain a given number
Spanish:
logaritmo
— The power to which a given base number must be raised in order to obtain a given number
Swedish:
logaritm
— The power to which a given base number must be raised in order to obtain a given number
Tagalog:
logpaulit
— The power to which a given base number must be raised in order to obtain a given number
Tamil:
மடக்கை
(maṭakkai)
— The power to which a given base number must be raised in order to obtain a given number
Thai:
ลอการิทึม
(lɔɔ-gaa-rí-tʉm)
— The power to which a given base number must be raised in order to obtain a given number
Turkish:
logaritma
— The power to which a given base number must be raised in order to obtain a given number
Ottoman Turkish:
لوغاریتمه
(logaritma)
— The power to which a given base number must be raised in order to obtain a given number
Ukrainian:
логари́фм
(loharýfm)
— The power to which a given base number must be raised in order to obtain a given number
Ukrainian:
логари́тм
(loharýtm)
— The power to which a given base number must be raised in order to obtain a given number
Vietnamese:
đối số
— The power to which a given base number must be raised in order to obtain a given number
Vietnamese:
lôga
— The power to which a given base number must be raised in order to obtain a given number
Vietnamese:
lôgarit
— The power to which a given base number must be raised in order to obtain a given number
Vietnamese:
lô-ga-rít
— The power to which a given base number must be raised in order to obtain a given number
Welsh:
logarithm
— The power to which a given base number must be raised in order to obtain a given number
Yiddish:
לאָגאַריטם
(logaritm)
— The power to which a given base number must be raised in order to obtain a given number
