Chapter 12 - Section 12.8 - Exponential and Logarithmic Equations and Problem Solving - Exercise Set - Page 896: 19

$x=\dfrac{3}{4}$

$\log_{2}6-\log_{2}x=3$ Combine $\log_{2}6-\log_{2}x$ as the $\log$ of a division: $\log_{2}\dfrac{6}{x}=3$ Rewrite this equation in exponential form: $2^{3}=\dfrac{6}{x}$ $\dfrac{6}{x}=8$ Solve for $x$: $\dfrac{x}{6}=\dfrac{1}{8}$ $x=\dfrac{6}{8}$ $x=\dfrac{3}{4}$