# Logarithm definition

lôgə-rĭthəm, lŏgə-
Frequency:
The power to which a base must be raised to produce a given number. For example, if the base is 10, then the logarithm of 1,000 (written log 1,000 or log10 1,000) is 3 because 103 = 1,000.
See log.
(mathematics) For a number , the power to which a given base number must be raised in order to obtain . Written . For example, because and because .

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.

noun
The power to which a base, such as 10, must be raised to produce a given number. If nx = a, the logarithm of a, with n as the base, is x; symbolically, log n a = x. For example, 103 = 1,000; therefore, log10 1,000 = 3. The kinds most often used are the common logarithm (base 10), the natural logarithm (base e ), and the binary logarithm (base 2).
noun
(math.) The exponent expressing the power to which a fixed number (the base) must be raised in order to produce a given number (the antilogarithm): logarithms computed to the base 10 are often used for shortening mathematical calculations.
noun

Singular:
logarithm
Plural:
logarithms

## Origin of logarithm

• New Latin logarithmus Greek logos reason, proportion leg- in Indo-European roots Greek arithmos number ar- in Indo-European roots

### From American Heritage Dictionary of the English Language, 5th Edition

• From New Latin logarithmus, term coined by Scot mathematician John Napier from Ancient Greek λόγος (logos, “word, reason") and ἀριθμός (arithmos, “number").