Solve the equation $LaTeX: \displaystyle \log_{9}(x + 709)-\log_{9}(x + 61)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{9}\frac{x + 709}{x + 61} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 9$ gives $LaTeX: \displaystyle \frac{x + 709}{x + 61}=9$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 709=9 x + 549$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 20$ .