Answer
$x=3$
Work Step by Step
Combine like terms and rewrite using the definition of log. Then factor the side with $x$ to solve. $-7$ is not part of the domain, so $3$ is the answer.
$\log_2(x+5)+\log_2(x-1)=4$
$\log_2(x+5)(x-1)=4$
$16=x^2+4x-5$
$x^2+4x-21=0$
$(x+7)(x-3)=0$
$x=-7, x=3$
$x=3$
