# logarithm

## English

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### Pronunciation

• (US) IPA(key): /ˈlɑ.ɡə.ɹɪ.ð(ə)m/

### Etymology

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

### Noun

logarithm ‎(plural logarithms)

1. (mathematics) For a number $x$, the power to which a given base number must be raised in order to obtain $x$. Written $\log_b x$. For example, $\log_{10} 1000 = 3$ because $10^3 = 1000$ and $\log_2 16 = 4$ because $2^4 = 16$.
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.