Solve the equation $LaTeX: \displaystyle \log_{9}(x + 6541)-\log_{9}(x + 61)=2$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{9}\frac{x + 6541}{x + 61} = 2$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 9$ gives $LaTeX: \displaystyle \frac{x + 6541}{x + 61}=81$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 6541=81 x + 4941$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 20$ .