Chapter 12 - Section 12.8 - Exponential and Logarithmic Equations and Problem Solving - Exercise Set - Page 896: 26

$x=\dfrac{2}{35}$

$\log_{6}(x+2)-\log_{6}x=2$ Combine $\log_{6}(x+2)-\log_{6}x$ as the $\log$ of a division: $\log_{6}\dfrac{x+2}{x}=2$ Rewrite in exponential form: $6^{2}=\dfrac{x+2}{x}$ $\dfrac{x+2}{x}=36$ Take $x$ to multiply the right side of the equation: $x+2=36x$ Solve for $x$: $x-36x=-2$ $-35x=-2$ $x=\dfrac{-2}{-35}$ $x=\dfrac{2}{35}$