Solve the equation $LaTeX: \displaystyle \log_{8}(x + 32785)-\log_{8}(x + 81)=3$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{8}\frac{x + 32785}{x + 81} = 3$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 8$ gives $LaTeX: \displaystyle \frac{x + 32785}{x + 81}=512$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 32785=512 x + 41472$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -17$ .