#### Answer

$x_{1}=-4;x_{2}=25$

#### Work Step by Step

$\log x+\log \left( x-21\right) =\log 100\Rightarrow \log \left( x\left( x-21\right) \right) =\log 100$
$\Rightarrow x^{2}-21x=100\Rightarrow x^{2}-21x-100=0\Rightarrow \left( x+4\right) \left( x-25\right) =0;x_{1}=-4;x_{2}=25$