Question

solve each equation

$9^{2x}{27}^{x^2}=3^{-1}$

Short answer

The value of x for which the above equation is valid are :

$-3,-1$

Step-by-step solution

Step 1. Given equation

$9^{2x}{27}^{x^2}=3^{-1}$

Step 2. Solving exponentially

$$\begin{gathered} 9^{2x}{27}^{x^2}=3^{-1} \\ {3}^{6x}{3}^{3x^2}=3^{-1} \\ {3}^{(3x^2+6x)}=3^{-1} \\ \Rightarrow 3x^2+6x=-1 \\ \Rightarrow x=-1,-3 \end{gathered}$$