#### Answer

$2$

#### Work Step by Step

$\log \left( x-10\right) -\log \left( x-6\right) =\log 2\Rightarrow \log \left( x-10\right) =\log 2+\log \left( x-6\right) \Rightarrow$
$ \log \left( x-10\right) =\log \left[ 2\times \left( x-6\right) \right] \Rightarrow x-10=2x-12\Rightarrow x=2$