logarithm

log·a·ri·thm
L1O1G2A1R1I1T1H4M3
UK/ˈlɒɡ.ə.ɹɪ.ð(ə)m/UK/ˈlɔɡ.ə.ɹɪ.ð(ə)m/US/ˈlɑ.ɡə.ɹɪ.ð(ə)m/US/ˈlɑ.ɡəɹ.ɹɪ.ðəm/

noun

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.

“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.”

Similar
log
OriginNew Latin logarithmus ← Ancient Greek λόγος →
Less commonScrabble 15
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Meanings

nounlogarithm (plural logarithms)

plural logarithms

  1. mathematicsFor 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.

    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.

    Synonyms: log

Synonyms & antonyms

nounFor 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.

Similar
log

More synonyms by meaning

nounthe exponent required to produce a given number

Similar
log
Broader
exponentpowerindex
Also see
log

Synonym sets from Open English WordNet, CC BY 4.0.

Origin

  1. Ancient Greekλόγος“ratio, proportion”
  2. New Latinlogarithmus
  3. Englishlogarithm

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.

More words from New Latin, Ancient Greek

Full word history & related roots →

Translations

Arabic أَسِيس, لُوغَارِثْم
  • أَسِيس (ʔasīs)The power to which a given base number must be raised in order to obtain a given number
  • لُوغَارِثْم (lūḡāriṯm)The power to which a given base number must be raised in order to obtain a given number
Bulgarian логаритъм
  • логаритъм (logarităm)The power to which a given base number must be raised in order to obtain a given number
Catalan logaritme
  • logaritmeThe power to which a given base number must be raised in order to obtain a given number
Chinese Mandarin 對數 /对数
  • 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
  • logaritmusThe power to which a given base number must be raised in order to obtain a given number
Danish logaritme
  • logaritmeThe power to which a given base number must be raised in order to obtain a given number
Dutch logaritme
  • logaritmeThe power to which a given base number must be raised in order to obtain a given number
Esperanto logaritmo
  • logaritmoThe power to which a given base number must be raised in order to obtain a given number
Finnish logaritmi
  • logaritmiThe power to which a given base number must be raised in order to obtain a given number
French logarithme
  • logarithmeThe power to which a given base number must be raised in order to obtain a given number
German Logarithmus
  • LogarithmusThe power to which a given base number must be raised in order to obtain a given number
Greek λογάριθμος
  • λογάριθμος (logárithmos)The power to which a given base number must be raised in order to obtain a given number
Hawaiian huhui helu
  • huhui heluThe power to which a given base number must be raised in order to obtain a given number
Hindi लघुगणक
  • लघुगणक (laghugṇak)The power to which a given base number must be raised in order to obtain a given number
Hungarian logaritmus
  • logaritmusThe power to which a given base number must be raised in order to obtain a given number
Icelandic logri
  • logriThe power to which a given base number must be raised in order to obtain a given number
Indonesian logaritma
  • logaritmaThe power to which a given base number must be raised in order to obtain a given number
Italian logaritmo
  • logaritmoThe power to which a given base number must be raised in order to obtain a given number
Japanese 対数
  • 対数 (taisū)The power to which a given base number must be raised in order to obtain a given number
Korean 로그, 대수
  • 로그 (rogeu)The power to which a given base number must be raised in order to obtain a given number
  • 대수 (daesu)The power to which a given base number must be raised in order to obtain a given number
Latin logarithmus
  • logarithmusThe power to which a given base number must be raised in order to obtain a given number
Latvian logaritms
  • logaritmsThe power to which a given base number must be raised in order to obtain a given number
Māori taupū kōaro, pūkōaro
  • taupū kōaroThe power to which a given base number must be raised in order to obtain a given number
  • pūkōaroThe power to which a given base number must be raised in order to obtain a given number
Norwegian Bokmål logaritme
  • logaritmeThe power to which a given base number must be raised in order to obtain a given number
Polish logarytm
  • logarytmThe power to which a given base number must be raised in order to obtain a given number
Portuguese logaritmo
  • logaritmoThe power to which a given base number must be raised in order to obtain a given number
Punjabi ਲਘੂਗਣਕ
  • ਲਘੂਗਣਕ (laghūgṇak)The power to which a given base number must be raised in order to obtain a given number
Romanian logaritm
  • logaritmThe power to which a given base number must be raised in order to obtain a given number
Russian логари́фм
  • логари́фм (logarífm)The power to which a given base number must be raised in order to obtain a given number
Spanish logaritmo
  • logaritmoThe power to which a given base number must be raised in order to obtain a given number
Swedish logaritm
  • logaritmThe power to which a given base number must be raised in order to obtain a given number
Tagalog logpaulit
  • logpaulitThe power to which a given base number must be raised in order to obtain a given number
Tamil மடக்கை
  • மடக்கை (maṭakkai)The power to which a given base number must be raised in order to obtain a given number
Thai ลอการิทึม
  • 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
  • logaritmaThe power to which a given base number must be raised in order to obtain a given number
Ukrainian логари́фм, логари́тм
  • логари́фм (loharýfm)The power to which a given base number must be raised in order to obtain a given number
  • логари́тм (loharýtm)The power to which a given base number must be raised in order to obtain a given number
Vietnamese đối số, lôga
  • đối sốThe power to which a given base number must be raised in order to obtain a given number
  • lôgaThe power to which a given base number must be raised in order to obtain a given number
  • lôgaritThe power to which a given base number must be raised in order to obtain a given number
  • lô-ga-rítThe power to which a given base number must be raised in order to obtain a given number
Welsh logarithm
  • logarithmThe power to which a given base number must be raised in order to obtain a given number
Yiddish לאָגאַריטם
  • לאָגאַריטם (logaritm)The power to which a given base number must be raised in order to obtain a given number

Rhymes & wordplay

Anagrams

algorithmmithralog
Cite this entry
APA

logarithm. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/logarithm

MLA

“logarithm.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/logarithm. Accessed November 2, 2026.

Chicago

WatkinsX Dictionary, s.v. “logarithm,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/logarithm.

Source: logarithm on Wiktionary, CC BY-SA 4.0.