Solve the equation $LaTeX: \displaystyle \log_{4}(x + 1041)-\log_{4}(x + 33)=3$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{4}\frac{x + 1041}{x + 33} = 3$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 4$ gives $LaTeX: \displaystyle \frac{x + 1041}{x + 33}=64$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 1041=64 x + 2112$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -17$ .