Solve the equation $LaTeX: \displaystyle \log_{9}(x + 748)-\log_{9}(x + 100)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{9}\frac{x + 748}{x + 100} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 9$ gives $LaTeX: \displaystyle \frac{x + 748}{x + 100}=9$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 748=9 x + 900$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -19$ .