Answer
$x=-\dfrac{42}{23}$
Work Step by Step
Using the properties of logarithms and since $\log_b x=y$ is equivalent to $b^y=x$, then,
\begin{array}{l}
\log_6 x-\log_6 (4x+7)=1\\\\
\log_6 \dfrac{x}{4x+7}=1\\\\
\dfrac{x}{4x+7}=6^1\\\\
x=6(4x+7)\\\\
x=24x+42\\\\
-23x=42\\\\
x=-\dfrac{42}{23}
.\end{array}
