logarithm

logarithm

English

Etymology

From New Latin logarithmus, term coined by Scot mathematician John Napier from Ancient Greek λόγος (lógos, “word, reason”) and ἀριθμός (arithmós, “number”); compare rational number, from analogous Latin.

Pronunciation

• (US) IPA^(key): /ˈlɑ.ɡə.ɹɪ.ð(ə)m/, /ˈlɑɡəɹ.ɹɪ.ðəm/, /ˈlɑɡ.ə.ɹɪðm/, /ˈlɑɡ.əɹ.ɹɪðm/
• Hyphenation: log‧a‧ri‧thm

Noun

logarithm (plural logarithms)

1. (mathematics) For a number ${\\displaystyle x}$, the power to which a given base number must be raised in order to obtain ${\\displaystyle x}$. Written ${\\displaystyle \\log _{b}x}$. For example, ${\\displaystyle \\log _{10}1000=3}$ because ${\\displaystyle 10^{3}=1000}$ and ${\\displaystyle \\log _{2}16=4}$ because ${\\displaystyle 2^{4}=16}$.

   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

Derived terms

• antilogarithm
• binary logarithm
• common logarithm
• log
• logarithmancy
• logarithmic
• Napierian logarithm
• natural logarithm

 

Translations

The power to which a given base number must be raised in order to obtain a given number

Arabic: لُوغَارِثْم‎ m (luḡariṯm) Armenian: լոգարիթմ (hy) (logaritʿm) Bulgarian: логаритъм (bg) m (logaritǎm) Catalan: logaritme (ca) m Chinese: Mandarin: 對數／对数 (zh) (duìshù) Min Nan: 對數 (zh-min-nan) (tùi-sò͘), 對數 (zh-min-nan) (tuì-siàu) (Taiwanese) Czech: logaritmus (cs) m Danish: logaritme c Dutch: logaritme (nl) n Esperanto: logaritmo (eo) Finnish: logaritmi (fi) French: logarithme (fr) m Galician: logaritmo (gl) m Georgian: ლოგარითმი (logaritmi) German: Logarithmus (de) m Greek: λογάριθμος (el) m (logárithmos) Gujarati: લઘુગણક (laghugṇak) Hawaiian: huhui helu Hindi: लघुगणक (laghugṇak) Hungarian: logaritmus (hu) Icelandic: logri m Italian: logaritmo (it) m Japanese: 対数 (ja) (たいすう, taisū) Kannada: ಪೆರ್ಚುಪಟ್ಟು (kn) (percupaṭṭu), ಪಟ್ಟೇರುಕ (kn) (paṭṭēruka), ಲಘುಗಣಕ (kn) (laghugaṇaka) Khmer: លោការីត (lookaariit) Korean: 로그 (ko) (rogeu), 대수(對數) (ko) (daesu) Latin: logarithmus Latvian: logaritms m Macedonian: логари́там m (logarítam) Maori: taupū kōaro, pūkōaro Norwegian: Bokmål: logaritme (no) m Nynorsk: logaritme m Polish: logarytm (pl) m Portuguese: logaritmo (pt) m Punjabi: ਲਘੂਗਣਕ (laghūgṇak) Romanian: logaritm (ro) m Russian: логари́фм (ru) m (logarífm) Serbo-Croatian: logaritam (sh) m Shona: mhetapawa, davanharu Sinhalese: ලඝු ගණක (laghu gaṇaka) Slovene: logaritem (sl) m Spanish: logaritmo (es) m Swedish: logaritm (sv) c Tagalog: logpaulit Tamil: மடக்கை (ta) (maṭakkai) Thai: ลอการิทึม (logaaríteum) Turkish: logaritma (tr) Ukrainian: логари́фм (uk) m (loharýfm), логари́тм m (loharýtm) Vietnamese: đối số (對數), lôga, lôgarit, lô-ga-rít (vi) Yiddish: לאָגאַריטם‎ m (logaritm)

See also

Other terms used in arithmetic operations:

• successor
• addition, summation:

  (augend) + (addend) = (total)

  (summand) + (summand) + (summand)... = (sum)

• subtraction:

  (minuend) − (subtrahend) = (difference)

• multiplication, factorization:

  (multiplier) × (multiplicand) = (product)

  (factor) × (factor) × (factor)... = (product)

• division:

  (dividend) ÷ (divisor) = (quotient)

  (numerator) / (denominator) = (quotient)

  Or sometimes = (quotient) with (remainder) remaining

• exponentiation:

  (base) ^(exponent) = (power)

• root extraction:

  ^(degree) √ (radicand) = (root)

• logarithmization:

  log_(base) (antilogarithm) = (logarithm)

Advanced hyperoperations: tetration, pentation, hexation

• ln
• characteristic
• mantissa

Anagrams

• algorithm, mithralog