Answer
$x=\displaystyle \frac{17}{2}$
Work Step by Step
First, the solutions must satisfy $\left\{\begin{array}{l}
x+5\gt 0\\
x-4\gt 0
\end{array}\right.\quad \Rightarrow x\gt 4\qquad (*)$
in order for the equation to be defined.
LHS: Apply$ \displaystyle \quad\log_{a}\frac{M}{N}=\log_{a}M-\log_{a}N$
$\displaystyle \log_{12}[\frac{x+5}{x-4}]=\log_{12}3$
... apply the principle of logarithmic equality
$\displaystyle \frac{x+5}{x-4}=3$
$x+5=3(x-4)$
$x+5=3x-12$
$-2x=-17$
$x=\displaystyle \frac{17}{2}\qquad $... satisfies (*), and is a valid solution.
