Log base 4 of 32 is equal to 5/2.
What a log is looking for is what number do we have to raise 4 to in order to get 32. Since it is not an exact multiply of 4, we have to look for fractions. Since we know that 2 can multiply directly to 32, we would simply take the square root of 4. This can be done by raising 4 to the 1/2.
Now that we have 2, we know that raising that to the 5th power would give us 32. So we'll take that answer and the 1/2 from before and multiply them together to get the final answer.
5*1/2 = 5/2.