Solve the equation $LaTeX: \displaystyle \log_{9}(x + 6554)-\log_{9}(x + 74)=2$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{9}\frac{x + 6554}{x + 74} = 2$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 9$ gives $LaTeX: \displaystyle \frac{x + 6554}{x + 74}=81$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 6554=81 x + 5994$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 7$ .