Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.3 Logarithmic Functions - 4.3 Exercises - Page 447: 109

See explanations.

Step 1. Let $p=log_ax$ and $q=log_ay$, we have $x=a^p$ and $y=a^q$ Step 2. We have $\frac{x}{y}=\frac{a^p}{a^q}=a^{p-q}$, thus $p-q=log_a(\frac{x}{y})$ Step 3. Combine the above, we have $log_ax-log_ay=log_a(\frac{x}{y})$ or $log_a(\frac{x}{y})=log_ax-log_ay$