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1. Determine the value of $lo g_{3 \sqrt{2}} (\frac{1}{18})$ is = ?

A. 2

B. -2

C. $\sqrt{2}$

D. $\sqrt{3}$

Solution:

\begin{aligned} lo g_{3 \sqrt{2}} (\frac{1}{18}) \\ = lo g_{3 \sqrt{2}} (\frac{1}{{(3 \sqrt{2})}^{2}}) \\ = lo g_{3 \sqrt{2}} {(3 \sqrt{2})}^{- 2} \\ = (- 2) lo g_{3 \sqrt{2}} 3 \sqrt{2} \\ = - 2 \end{aligned}

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