Solve the equation $LaTeX: \displaystyle \log_{2}(x + 29)-\log_{2}(x + 17)=2$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{2}\frac{x + 29}{x + 17} = 2$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 2$ gives $LaTeX: \displaystyle \frac{x + 29}{x + 17}=4$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 29=4 x + 68$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -13$ .