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Examveda

If $${\log _3}x + {\log _{\underline 9 }}{x^2} + {\log _{27}}{x^3}$$     $$ = 9,$$  then x equals to -

A. 3

B. 9

C. 27

D. None of these

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & {\log _3}x + {\log _{\underline 9 }}{x^2} + {\log _{27}}{x^3} = 9 \cr & \Rightarrow {\log _3}x + {\log _{32}}{x^2} + {\log _{33}}{x^3} = 9 \cr & \Rightarrow {\log _3}x + \frac{2}{2}{\log _3}x + \frac{3}{3}{\log _3}x = 9 \cr & \Rightarrow 3{\log _3}x = 9 \cr & \Rightarrow {\log _3}x = 3 \cr & \Rightarrow x = {3^3} = 27 \cr} $$

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