Answer
$\log_3\dfrac{x+7}{4x+6}$
Work Step by Step
Using the properties of logarithms, the given expression, $
\log_3(x+7)-\log_3(4x+6)
$, is equivalent to
\begin{align*}\require{cancel}
&
\log_3\dfrac{x+7}{4x+6}
&(\text{use }\log_b \dfrac{x}{y}=\log_b x-\log_b y)
.\end{align*}
Hence, the expression $
\log_3(x+7)-\log_3(4x+6)
$ is equivalent to $
\log_3\dfrac{x+7}{4x+6}
$.
