Set 7: Exponential Functions (Intermediate)

Choice A is correct. Choice A is the correct answer. Rewrite with same base and solve. 1. Rewrite: $9= 3^2$, so $9^{x-1} = (3^2)^{x-1} = 3^{2(x-1)} = 3^{2 x-2}$. 2. Equation: $3^{x+2} = 3^{2 x-2}$. 3. Equal bases: $x + 2 = 2 x - 2$. 4. Solve: $2+ 2 = 2 x - x$, 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.