If b = a, then log base b of a^n is equal to n.
To explain this in simple terms, let's first define what a logarithm is. A logarithm is simply the power to which a number (called the base) must be raised in order to get another number. For example, if we have the logarithm base 2 of 8, this means "what power must we raise 2 to in order to get 8?" The answer is 3, because 2^3 = 8.
Now, in the given expression log base b of a^n, we have a base of b and an exponent of n. If b = a, this means that the base and the exponent are the same number. So we can rewrite the expression as log base a of a^n.
What power must we raise a to in order to get a^n? The answer is n, because a^n is simply a multiplied by itself n times. So the logarithm base a of a^n is equal to n.
Therefore, if b = a, then log base b of a^n is equal to n. The answer is (a) n.