Solve the equation $LaTeX: \displaystyle \log_{2}(x + 21)-\log_{2}(x + 13)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{2}\frac{x + 21}{x + 13} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 2$ gives $LaTeX: \displaystyle \frac{x + 21}{x + 13}=2$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 21=2 x + 26$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -5$ .