Chapter 12 - Exponential Functions and Logarithmic Functions - 12.4 Properties of Logarithmic Functions - 12.4 Exercise Set - Page 810: 57

$\log_a (x-3)$

Using the properties of logarithms, the given expression, $ \log_a (x^2-9)-\log_a (x+3) ,$ simplifies to \begin{array}{l}\require{cancel} \log_a \dfrac{x^2-9}{x+3} \\\\= \log_a \dfrac{(x+3)(x-3)}{x+3} \\\\= \log_a \dfrac{(\cancel{x+3})(x-3)}{\cancel{x+3}} \\\\= \log_a (x-3) .\end{array}