The master method only applies to a particular family of recurrences of the form:

sub problems, each of size

Where:

(problem should get smaller)
for ( is asymptotically positive)

Master Method Cases

There are 3 main cases to consider when using the master method:

If where then
If where then
If where then

In other words, the average case (see Big-Theta Notation) can be directly known by solving which of these three cases a recurrence falls into.

Master Method Example

Here , , , and .
Since for , case 1 of the master theorem applies.
So the solution is .
Here , ,