Choice A is the correct answer. Rewrite with same base and solve.

1. Rewrite: $9 = 3^2$, so $9^{x-1} = (3^2)^{x-1} = 3^{2(x-1)} = 3^{2x-2}$.
2. Equation: $3^{x+2} = 3^{2x-2}$.
3. Equal bases: $x + 2 = 2x - 2$.
4. Solve: $2 + 2 = 2x - x$, so $4 = x$.
5. Verify: $3^{4+2} = 3^6 = 729$ and $9^{4-1} = 9^3 = 729$ ✓

💡 Strategic Tip: Always rewrite to a common base before equating exponents.

Choice B is incorrect because$3^4 = 81$ and $9^1 = 9$, not equal. Choice C is incorrect because$3^5 = 243$ and $9^2 = 81$, not equal. Choice D is incorrect because$3^3 = 27$ and $9^0 = 1$, not equal.