# logarithm

## English

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### 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.