Solve the equation $LaTeX: \displaystyle \log_{10}(x + 99987)-\log_{10}(x + 9987)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{10}\frac{x + 99987}{x + 9987} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 10$ gives $LaTeX: \displaystyle \frac{x + 99987}{x + 9987}=10$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 99987=10 x + 99870$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 13$ .