Solve the equation $LaTeX: \displaystyle \log_{7}(x + 2407)-\log_{7}(x + 349)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{7}\frac{x + 2407}{x + 349} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 7$ gives $LaTeX: \displaystyle \frac{x + 2407}{x + 349}=7$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 2407=7 x + 2443$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -6$ .