Answer
$\pm\sqrt 3\approx\pm1.732$
Work Step by Step
Step 1. Rewrite the equation as $log_{13}(x+2)^2=log_{13}(4x+7)$
Step 2. Thus $(x+2)^2=4x+7 \longrightarrow x^2=3 \longrightarrow x=\pm\sqrt 3$.
Step 3. Check answers, $x=\pm\sqrt 3\approx\pm1.732$ fits the original equation.
