#### Answer

$x_{1}=0;x_{2}=\dfrac {5}{2}$

#### Work Step by Step

$\ln \left( 4x-2\right) -\ln 4=-\ln \left( x-2\right) \Rightarrow \ln \left( 4x-2\right) +\ln \left( x-2\right) =\ln 4$
$\ln \left( 4x-2\right) \left( x-2\right) =\ln 4\Rightarrow \left( 4x-2\right) \left( x-2\right) =4$
$4x^{2}-10x+4=4\Rightarrow 4x^{2}=10x\Rightarrow x_{1}=0;x_{2}=\dfrac {5}{2}$