Solve the equation $LaTeX: \displaystyle \log_{8}(x + 532)-\log_{8}(x + 84)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{8}\frac{x + 532}{x + 84} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 8$ gives $LaTeX: \displaystyle \frac{x + 532}{x + 84}=8$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 532=8 x + 672$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -20$ .