If _x ( 916 ) = - 1/2, then x is equal to:

Answer: Option D

$$\begin{array}{rl}& {\log }_x\left(\frac{9}{16}\right)=-\frac{1}{2}\\ & \Rightarrow x^{-\frac{1}{2}}=\frac{9}{16}\\ & \Rightarrow \frac{1}{\sqrt{x}}=\frac{9}{16}\\ & \Rightarrow \sqrt{x}=\frac{16}{9}\\ & \Rightarrow x={\left(\frac{16}{9}\right)}^2\\ & \Rightarrow x=\frac{256}{81}\end{array}$$