Solve the equation $LaTeX: \displaystyle \log_{3}(x + 259)-\log_{3}(x + 25)=3$ .

Using the quotient property of logarithms gives $LaTeX: \displaystyle \log_{3}\frac{x + 259}{x + 25} = 3$ . Making both sides of the equation exponents on the base $LaTeX: \displaystyle 3$ gives $LaTeX: \displaystyle \frac{x + 259}{x + 25}=27$ . Clearing the fractions by multiplying by the LCD gives $LaTeX: \displaystyle x + 259=27 x + 675$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = -16$ .