Determine the value of lo g_3 2 ( 118 ) is = ?

Answer: Option B

$$\begin{array}{rl}& \text{lo}{\text{g}}_{3\sqrt{2}}\left(\frac{1}{18}\right)\\ & =\text{lo}{\text{g}}_{3\sqrt{2}}\left(\frac{1}{{\left(3\sqrt{2}\right)}^2}\right)\\ & =\text{lo}{\text{g}}_{3\sqrt{2}}{\left(3\sqrt{2}\right)}^{-2}\\ & =\left(-2\right)\text{lo}{\text{g}}_{3\sqrt{2}}3\sqrt{2}\\ & =-2\end{array}$$