# Chapter 12 - Exponential Functions and Logarithmic Functions - 12.4 Properties of Logarithmic Functions - 12.4 Exercise Set - Page 810: 58

$\log_a \dfrac{2}{x-5}$

#### Work Step by Step

Using the properties of logarithms, the given expression, $\log_a (2x+10)-\log_a (x^2-25) ,$ simplifies to \begin{array}{l}\require{cancel} \log_a \dfrac{2x+10}{x^2-25} \\\\= \log_a \dfrac{2(x+5)}{(x+5)(x-5)} \\\\= \log_a \dfrac{2(\cancel{x+5})}{(\cancel{x+5})(x-5)} \\\\= \log_a \dfrac{2}{x-5} .\end{array}

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