Perform the indicated operations on the resulting expressions if the given changes are made in the original expressions of the indicated examples of this section.

In Example 7, change the 2 to 3.

Data from Example 7

Use the basic properties of logarithms to solve the following equation for y in terms of x: log_b y = 2 log_b x + log_b a.  Using Eq. (13.9) and then Eq. (13.7), we have log_b y = log_b (x²) + log_b a = log_b (ax²).

Because we have the logarithm to the base b of different expressions on each side of the resulting equation, the expressions must be equal. Therefore, y = ax²