jmc

If $3^{2x^2-5x+2}=3^{2x^2+7x-4}$, then $2x^2-5x+2=2x^2+7x-4$. We can eliminate the $2x^2$ term from each side and solve $-5x+2=7x-4$ for $x$ to get $x=\boxed{\frac{1}{2}}$.