Solve the equation $LaTeX: \displaystyle \log_{8}(x + 4107)-\log_{8}(x + 523)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{8}\frac{x + 4107}{x + 523} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 8$ gives $LaTeX: \displaystyle \frac{x + 4107}{x + 523}=8$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 4107=8 x + 4184$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -11$ .