Answer
$x=2$
Work Step by Step
1. Use product rule, we have $log_2[x(x+2)]=3\longrightarrow x(x+2)=2^3\longrightarrow x^2+2x-8=0\longrightarrow (x+4)(x-2)=0$, thus $x=-4,2$
2. Check the answers in the original equation, we find only $x=2$ fits.
