Solve the equation $LaTeX: \displaystyle \log_{5}(x + 120)-\log_{5}(x + 20)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{5}\frac{x + 120}{x + 20} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 5$ gives $LaTeX: \displaystyle \frac{x + 120}{x + 20}=5$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 120=5 x + 100$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 5$ .