Determine the value of $${\text{lo}}{{\text{g}}_{3\sqrt 2 }}\left( {\frac{1}{{18}}} \right)$$   is = ?

A. 2

B. -2

C. $$\sqrt 2 $$

D. $$\sqrt 3 $$

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & {\text{lo}}{{\text{g}}_{3\sqrt 2 }}\left( {\frac{1}{{18}}} \right)\, \cr & = {\text{lo}}{{\text{g}}_{3\sqrt 2 }}\left( {\frac{1}{{{{\left( {3\sqrt 2 } \right)}^2}}}} \right)\, \cr & = {\text{lo}}{{\text{g}}_{3\sqrt 2 }}{\text{ }}{\left( {3\sqrt 2 } \right)^{ - 2}} \cr & = \left( { - 2} \right){\text{lo}}{{\text{g}}_{3\sqrt 2 }}3\sqrt 2 \cr & = - 2 \cr} $$