Solve the equation $LaTeX: \displaystyle \log_{5}(x + 650)-\log_{5}(x + 150)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{5}\frac{x + 650}{x + 150} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 5$ gives $LaTeX: \displaystyle \frac{x + 650}{x + 150}=5$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 650=5 x + 750$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -25$ .