If _3x + _9x^2 + _27x^3 = 9, then x equals to -

Answer: Option C

$$\begin{array}{rl}& \Rightarrow {\log }_{3}x+{\log }_9{x}^2+{\log }_{27}{x}^3=9\\ & \Rightarrow {\log }_{3}x+{\log }_{3^2}{x}^2+{\log }_{3^3}{x}^3=9\\ & \Rightarrow {\log }_{3}x+\frac{2}{2}{\log }_{3}x+\frac{3}{3}{\log }_{3}x=9\\ & \Rightarrow 3{\log }_{3}x=9\\ & \Rightarrow {\log }_{3}x=3\\ & \Rightarrow x=3^3=27\end{array}$$