Answer
$x=3$ and $x=-2$
Work Step by Step
$\log_{2}(x^{2}-x-2)=2$
Write this equation in exponential form:
$x^{2}-x-2=2^{2}$
$x^{2}-x-2=4$
Take the $4$ to the left side of the equation:
$x^{2}-x-2-4=0$
$x^{2}-x-6=0$
Solve by factoring:
$(x-3)(x+2)=0$
We get two solutions:
$x=3$ and $x=-2$