We know that 2^{4} = 16 and also that 2 is referred to as the base, 4 as the index or power or the exponent. The same if expressed in terms of logarithms would be log_{2}16 = 4 and is read as the logarithm of 16 to base 2 is 4. Hence we define the logarithm of a number to a given base as the index or the power to which the base should be raised in order to yield the given number. We look at the following example.
What would be the value of log_{12}144?
If we assume x to be the value then
log_{12}144 = x
This is the same as 144 = 12^{x}. That is, 12 should be raised or in other words multiplied by itself so that the resultant value is 144. We find that 12 when multiplied twice would give 144. That is, the value of x = 2. This gives the value of log_{12}144 as 2.