Solve the equation $LaTeX: \displaystyle \log_{8}(x + 32774)-\log_{8}(x + 70)=3$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{8}\frac{x + 32774}{x + 70} = 3$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 8$ gives $LaTeX: \displaystyle \frac{x + 32774}{x + 70}=512$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 32774=512 x + 35840$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -6$ .