Solve the equation $LaTeX: \displaystyle \log_{3}(x + 76)-\log_{3}(x + 4)=2$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{3}\frac{x + 76}{x + 4} = 2$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 3$ gives $LaTeX: \displaystyle \frac{x + 76}{x + 4}=9$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 76=9 x + 36$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 5$ .