Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 337: 35

$4\sqrt 2-2$

1. $2log_6(x+2)=3log_6(2)+log_6(4) \Longrightarrow 2log_6(x+2)=log_6(2^3(4))\Longrightarrow log_6(x+2)=\frac{1}{2}log_6(32)\Longrightarrow x+2=\sqrt {32} \Longrightarrow x=4\sqrt 2-2$. 2. Check only $x=4\sqrt 2-2$ fits.