Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 469: 61

$2$

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