Solve the equation $LaTeX: \displaystyle \log_{6}(x + 7801)-\log_{6}(x + 61)=3$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{6}\frac{x + 7801}{x + 61} = 3$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 6$ gives $LaTeX: \displaystyle \frac{x + 7801}{x + 61}=216$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 7801=216 x + 13176$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -25$ .