Solve the equation $LaTeX: \displaystyle \log_{8}(x + 32753)-\log_{8}(x + 49)=3$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{8}\frac{x + 32753}{x + 49} = 3$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 8$ gives $LaTeX: \displaystyle \frac{x + 32753}{x + 49}=512$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 32753=512 x + 25088$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 15$ .