Question

$\frac{3^x\times 3}{3^{2x-2}}=9^{-2}$, find $x$.

Answer 1

Given

$\frac{3^x\times 3^1}{3^{2x-2}}=9^{-2}$

$\Rightarrow \frac{3^{x+1}}{3^{2x-2}}=9^{-2}$

$\Rightarrow 3^{x+1-(2x-2)}=9^{-2}$

$\Rightarrow 3^{x+1-2x+2}={3^2}^{-2}$

$\Rightarrow 3^{-x+3}=3^{-4}$

Comparing the powers, we get

$\Rightarrow -x+3=-4$

$\Rightarrow x=7$