## Logarithm is the inverse operation to exponentiation

In mathematics, the logarithm is the inverse operation to exponentiation, just as division is the inverse of multiplication and vice versa. That means the logarithm of a number is the exponent to which another fixed number, the base, must be raised to produce that number. In the most simple case the logarithm counts repeated multiplication of the same factor; e.g., since

`1000 = 10 × 10 × 10 = 10`

, the “logarithm to base 10” of 1000 is 3. More generally, exponentiation allows any positive real number to be raised to any real power, always producing a positive result, so the logarithm can be calculated for any two positive real numbers^{3}`b`

and`x`

where`b`

is not equal to`1`

. The logarithm of`x`

to base`b`

, denoted`log`

(or_{b}(x)`log`

when no confusion is possible), is the unique real number_{b}x`y`

such that`b`

. For example,^{y}= x`log`

, as_{2}64 = 6`64 = 2`

.^{6}

Another example: When `N = a`

then ^{x}`x`

is equal to `log`

(or _{a} (N)`log`

)._{a} N

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