Solve the equation $LaTeX: \displaystyle \log_{2}(x - 17)-\log_{2}(x - 21)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{2}\frac{x - 17}{x - 21} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 2$ gives $LaTeX: \displaystyle \frac{x - 17}{x - 21}=2$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x - 17=2 x - 42$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 25$ .