Answer
$-1+\sqrt {1+e^4}\approx6.456$
Work Step by Step
Step 1. Rewrite the equation as $ln[(x)(x+2)]=4 \longrightarrow ln(x^2+2x)=4$
Step 2. Thus $x^2+2x=e^4\longrightarrow x^2+2x-e^4=0\longrightarrow x=\frac{-2\pm\sqrt {4+4e^4}}{2}\longrightarrow x=-1\pm\sqrt {1+e^4}$.
Step 3. Check answers, only $x=-1+\sqrt {1+e^4}\approx6.456$ fits the original equation.
