Solve the equation $LaTeX: \displaystyle \log_{5}(x + 3143)-\log_{5}(x + 643)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{5}\frac{x + 3143}{x + 643} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 5$ gives $LaTeX: \displaystyle \frac{x + 3143}{x + 643}=5$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 3143=5 x + 3215$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -18$ .