Solve the equation $LaTeX: \displaystyle \log_{10}(x + 9986)-\log_{10}(x + 986)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{10}\frac{x + 9986}{x + 986} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 10$ gives $LaTeX: \displaystyle \frac{x + 9986}{x + 986}=10$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 9986=10 x + 9860$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 14$ .