Solve $LaTeX: \displaystyle \log_{ 12 }(x + 18) + \log_{ 12 }(x + 1734) = 4$

Using the product rule for logarithms gives $LaTeX: \displaystyle \log_{ 12 }(\left(x + 18\right) \left(x + 1734\right))$ and rewriting in exponential form gives $LaTeX: \displaystyle \left(x + 18\right) \left(x + 1734\right) = 20736$ expanding and setting the equation equal to zero gives $LaTeX: \displaystyle x^{2} + 1752 x + 10476 = 0$ . Factoring gives $LaTeX: \displaystyle \left(x + 6\right) \left(x + 1746\right)=0$ . This gives two possible solutions $LaTeX: \displaystyle x=-1746$ or $LaTeX: \displaystyle x=-6$ . $LaTeX: \displaystyle x=-1746$ is an extraneous solution. The only soution is $LaTeX: \displaystyle x=-6$ .