Solve the equation $LaTeX: \displaystyle \log_{9}(x + 6586)-\log_{9}(x + 754)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{9}\frac{x + 6586}{x + 754} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 9$ gives $LaTeX: \displaystyle \frac{x + 6586}{x + 754}=9$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 6586=9 x + 6786$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -25$ .