Solve the equation $LaTeX: \displaystyle \log_{3}(x + 102)-\log_{3}(x + 30)=2$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{3}\frac{x + 102}{x + 30} = 2$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 3$ gives $LaTeX: \displaystyle \frac{x + 102}{x + 30}=9$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 102=9 x + 270$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -21$ .