Set 15: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. Rewrite with base 2 and solve. 1. Rewrite: $4= 2^2$ and $8= 2^3$. 2. Substitute: $(2^2)^x = (2^3)^{x-2}$. 3. Simplify: $2^{2 x} = 2^{3(x-2)} = 2^{3 x-6}$. 4. Equal bases: $2x = 3 x - 6$. 5. Solve: $-x = -6$, so $x = 6$. 6. Verify: $4^6 = 4096$ and $8^4 = 4096$ ✓ Strategic Tip: Convert to a common base (usually smallest prime). Choice B is incorrect because $4^4 = 256$ and $8^2 = 64$, not equal. Choice C is incorrect because this gives different values. Choice D is incorrect because $4^2 = 16$ and $8^0 = 1$, not equal.