Solve the equation $LaTeX: \displaystyle \log_{5}(x + 3126)-\log_{5}(x + 26)=3$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{5}\frac{x + 3126}{x + 26} = 3$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 5$ gives $LaTeX: \displaystyle \frac{x + 3126}{x + 26}=125$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 3126=125 x + 3250$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -1$ .