#### Answer

$6$

#### Work Step by Step

$\ln e^{\ln x}-\ln \left( x-4\right) =\ln 3\Rightarrow \ln x=\ln 3+\ln \left( x-4\right) $
$\Rightarrow \ln x=\ln \left[ 3\left( x-4\right) \right] \Rightarrow x=3\left( x-4\right) \Rightarrow 2x=12\Rightarrow x=6$