Solve the equation $LaTeX: \displaystyle \log_{2}(x - 8)-\log_{2}(x - 20)=2$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{2}\frac{x - 8}{x - 20} = 2$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 2$ gives $LaTeX: \displaystyle \frac{x - 8}{x - 20}=4$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x - 8=4 x - 80$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 24$ .