Answer
$\frac{-5+3\sqrt {5}}{2}\approx0.854$
Work Step by Step
Step 1. Rewrite the equation as $log_3[(x+1)(x+4)]=2 \longrightarrow log_3(x^2+5x+4)=2$
Step 2. Thus $x^2+5x+4=3^2\longrightarrow x^2+5x-5=0\longrightarrow x=\frac{-5\pm\sqrt {25+20}}{2}=\frac{-5\pm3\sqrt {5}}{2}$.
Step 3. Check answers, only $x=\frac{-5+3\sqrt {5}}{2}\approx0.854$ fits the original equation.
