Solve the equation $LaTeX: \displaystyle \log_{10}(x + 9991)-\log_{10}(x + 91)=2$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{10}\frac{x + 9991}{x + 91} = 2$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 10$ gives $LaTeX: \displaystyle \frac{x + 9991}{x + 91}=100$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 9991=100 x + 9100$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 9$ .