Solve the equation $LaTeX: \displaystyle \log_{5}(x + 107)-\log_{5}(x + 7)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{5}\frac{x + 107}{x + 7} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 5$ gives $LaTeX: \displaystyle \frac{x + 107}{x + 7}=5$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 107=5 x + 35$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 18$ .