Solve the equation $LaTeX: \displaystyle \log_{5}(x + 3123)-\log_{5}(x + 23)=3$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{5}\frac{x + 3123}{x + 23} = 3$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 5$ gives $LaTeX: \displaystyle \frac{x + 3123}{x + 23}=125$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 3123=125 x + 2875$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 2$ .