Answer
$-4+\sqrt {17}\approx0.123$
Work Step by Step
Step 1. Rewrite the equation as $log_2[(x+1)(x+7)]=3 \longrightarrow log_2(x^2+8x+7)=3$
Step 2. Thus $x^2+8x+7=2^3\longrightarrow x^2+8x-1=0\longrightarrow x=\frac{-8\pm\sqrt {64+4}}{2}=-4\pm\sqrt {17}$.
Step 3. Check answers, only $x=-4+\sqrt {17}\approx0.123$ fits the original equation.
