logarithm

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.

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

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.

• log

• common logarithm
• natural logarithm
• log
• logarithmancy
• logarithmic

• ln

• algorithm, mithralog