2015-II-32

Ans: A
The equation of the straight line in the figure is

$\begin{array}{rcl}
\dfrac{\log_3 y – 0}{\log_3 x -3} & = & \dfrac{2-0}{0-3} \\
\dfrac{\log_3 y}{\log_3 x -3} & = & \dfrac{-2}{3} \\
3\log_3 y & = & -2\log_3 x +6 \\
3\log_3 y +2 \log_3 x & = & 6\log_3 3 \\
\log_3 y^3 + \log_3 x^2 & = & \log_3 3^6 \\
\log_3 (x^2y^3) & = & \log_3 729 \\
x^2 y^3 & = & 729
\end{array}$