Perhaps the simplest way to think of a logarithm is as a
function that turns
multiplication into addition . For example, since
5 is said to be the logarithm base 2 of 32.
Correspondingly, since
3 is said to be the logarithm base 10 of 1000. The
ex pressions in (1) and (2) can also be
written, respectively:
Returning to (1), notice that
, etc. That is, the
answer may be obtained in a variety of ways by adding exponents rather than
performing
a large number of multiplications .
The formula for converting a relative frequency ratios to
cents employs a base 10 logarithm:
where
is the relative
frequency ratio, and c is cents.
It is much easier to compare the relative size of two
intervals using cents than using ratios. For
example, what is the difference in size between the just P5 (3:2) and the
piano's P5 
?
Using frequency ratios, it may be calculated in the following manner ( using
division ):
Contrastingly, (3) may be used to convert the frequency
ratios to cents first (and rounding to the
nearest cent), then the size of the interval may calculated using subtraction :
