Answer
$4$
Work Step by Step
$\log _{7}\left( 3x+2\right) -\log _{7}\left( x-2\right) =1\Rightarrow \log _{7}\dfrac {\left( 3x+2\right) }{\left( x-2\right) }=1\Rightarrow \dfrac {3x+2}{\left( x-2\right) }=7^{1}$
$\Rightarrow 3x+2=7\left( x-2\right) \Rightarrow 3x+2=7x-14\Rightarrow 4x=16\Rightarrow x=4$
