Precalculus, Chapter 3, 3.4, Section 3.4, Problem 8

Another method to solve this would be to get the same base because there is a rule that states if the bases are the same, then the exponent must equal each other.
Given,
x^a=x^b
Then,
a=b

This can be applied to this problem. Remember that 32 equals (1/2)^-5
Therefore, applying this rule,
(1/2)^x=(1/2)^-5
Using the variables from above,
a=x and b=-5
Therefore,
x=-5

Note that you should get the same answer if you used the ln method. If you don't then recheck your work because you must have made a mistake along the way!