A logarithm is the power to which a number must be raised in order to get some other number.

In other words, if a is a positive real number, other than 1 and a^m = x,

then we write: m = log_a x

and we say that the value of log x to the base a is m.

Ex 1. 10³ = 1000 => log₁₀ 1000 = 3

Ex 2. 3⁴ = 81 => log₃ 81 = 3

Ex 3. 2^-3 = 1/8 => log₂ (1/8) = -3