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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 = 103
, 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 numbersb
andx
whereb
is not equal to1
. The logarithm ofx
to baseb
, denotedlogb (x)
(orlogb x
when no confusion is possible), is the unique real numbery
such thatby = x
. For example,log2 64 = 6
, as64 = 26
.
Another example: When N = ax
then x
is equal to loga (N)
(or loga N
).
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