Solve the equation $LaTeX: \displaystyle \log_{6}(x + 1294)-\log_{6}(x + 34)=2$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{6}\frac{x + 1294}{x + 34} = 2$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 6$ gives $LaTeX: \displaystyle \frac{x + 1294}{x + 34}=36$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 1294=36 x + 1224$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 2$ .