Answer
$x=6$
Work Step by Step
Use the definition of the log function to solve for $x$. Rewrite the problem so that the base has the exponent of the opposite side and is equal to the log's number and/or variable. Then simplify the side with $x$ by factoring and then solving for $x$. $-3$ is not part of the domain, so $6$ is the only answer.
$\log_2(x+2)-\log_2(x-5)=3$
$\log_2(x+2)(x-5)=3$
$8=x^2-3x-10$
$x^2-3x-18=0$
$(x+3)(x-6)=0$
$x=-3, x=6$
$x=6$
