Solve the equation $LaTeX: \displaystyle \log_{7}(x + 16800)-\log_{7}(x + 336)=2$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{7}\frac{x + 16800}{x + 336} = 2$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 7$ gives $LaTeX: \displaystyle \frac{x + 16800}{x + 336}=49$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 16800=49 x + 16464$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 7$ .