#### Answer

$x_{1}=\dfrac {10}{3};x_{2}=1$

#### Work Step by Step

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