# Logarithm meaning

The power to which a base, such as 10, must be raised to produce a given number. If

*n*the logarithm of^{x}= a,*a,*with*n*as the base, is*x;*symbolically, log*For example, 10*_{n}a = x.^{3}= 1,000; therefore, log_{10}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

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

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 log

_{10}1,000) is 3 because 10^{3}= 1,000.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

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### Origin of logarithm

From New Latin

*logarithmus*, term coined by Scot mathematician John Napier from Ancient Greek*Î»ÏŒÎ³Î¿Ï‚*(logos, “word, reason") and*á¼€ÏÎ¹Î¸Î¼ÏŒÏ‚*(arithmos, “number").