Solve the equation $LaTeX: \displaystyle \log_{4}(x + 251)-\log_{4}(x + 11)=2$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{4}\frac{x + 251}{x + 11} = 2$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 4$ gives $LaTeX: \displaystyle \frac{x + 251}{x + 11}=16$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 251=16 x + 176$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 5$ .