Solve the equation $LaTeX: \displaystyle \log_{6}(x + 7758)-\log_{6}(x + 1278)=1$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{6}\frac{x + 7758}{x + 1278} = 1$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 6$ gives $LaTeX: \displaystyle \frac{x + 7758}{x + 1278}=6$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 7758=6 x + 7668$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 18$ .