#### Answer

$x_{1}=5;x_{2}=-\dfrac {2}{3}$

#### Work Step by Step

$\log x+\log \left( 3x-13\right) =\log 10\Rightarrow \log \left( x\left( 3x-13\right) \right) =\log 10$
$\Rightarrow x\left( 3x-13\right) =10\Rightarrow 3x^{2}-13x-10=0\Rightarrow \left( x-5\right) \left( 3x+2\right) =0\Rightarrow x_{1}=5;x_{2}=-\dfrac {2}{3}$