Solve $LaTeX: \displaystyle \log_{ 9 }(x + 12) + \log_{ 9 }(x + 732) = 4$

Using the product rule for logarithms gives $LaTeX: \displaystyle \log_{ 9 }(\left(x + 12\right) \left(x + 732\right))$ and rewriting in exponential form gives $LaTeX: \displaystyle \left(x + 12\right) \left(x + 732\right) = 6561$ expanding and setting the equation equal to zero gives $LaTeX: \displaystyle x^{2} + 744 x + 2223 = 0$ . Factoring gives $LaTeX: \displaystyle \left(x + 3\right) \left(x + 741\right)=0$ . This gives two possible solutions $LaTeX: \displaystyle x=-741$ or $LaTeX: \displaystyle x=-3$ . $LaTeX: \displaystyle x=-741$ is an extraneous solution. The only soution is $LaTeX: \displaystyle x=-3$ .