Solve the equation $LaTeX: \displaystyle \log_{9}(x + 59074)-\log_{9}(x + 106)=3$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{9}\frac{x + 59074}{x + 106} = 3$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 9$ gives $LaTeX: \displaystyle \frac{x + 59074}{x + 106}=729$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 59074=729 x + 77274$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -25$ .