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