logarithm

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

• (UK) IPA^(key): /ˈlɒɡ.ə.ɹɪ.ð(ə)m/, /ˈlɔɡ.ə.ɹɪ.ð(ə)m/

  • Audio (Southern England):

    (file)

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

logarithm (plural logarithms)

1. (mathematics) For a number ${\displaystyle x}$, the exponent by which a given base number must be raised in order to obtain the power ${\displaystyle x}$. 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 from one denomination to the next higher is either 0.3010 or 0.3979.

• log

Other terms used in arithmetic operations:

Advanced hyperoperations: tetration, pentation, hexation

• ln
• characteristic
• mantissa

• algorithm, mithralog