Chapter 5 - Exponential and Logarithmic Functions - 5.6 Logarithmic and Exponential Equations - 5.6 Assess Your Understanding - Page 311: 35

$-2+4\sqrt 2\approx3.657$

Step 1. Rewrite the equation as $log_{6}(x+2)^2=log_{6}(2^3)+log_{6}(4) \longrightarrow log_{6}(x+2)^2=log_{6}(32)$ Step 2. Thus $(x+2)^2=32\longrightarrow x+2=\pm4\sqrt 2 \longrightarrow x=-2\pm4\sqrt 2$. Step 3. Check answers, $x=-2+4\sqrt 2\approx3.657$ fits the original equation.