Logarithms are the inverse functions of exponentials. With two exceptions,
they look like 
where a is the base. This means that 
. In other words, the value of a logarithm (or log, for short) is the
power to which the base must be raised in order to get the number you are
taking the log of. For example, 
since 
. The two
exceptions in form are the common log, which has an understood base of 10,
written 
, and the natural log, which has base e, and is written
. Note that 
is only defined for x > 0. There is, in
fact, an asymptote at x = 0 and this function will pass through the point
(1,0).
Log functions have the following properties.
