Set 6: Exponential Functions

Choice A is correct. Choice A is the correct answer. Equal bases means equal exponents. 1. Given: $e^{x+3} = e^{2 x-1}$. 2. Equal bases: $x + 3 = 2 x - 1$. 3. Solve: $3+ 1 = 2 x - x$, so $x = 4$. 4. Verify: $e^{4+3} = e^7$ and $e^{2(4)-1} = e^7$ ✓ Strategic Tip: When bases match, set exponents equal. Choice B is incorrect because $e^5 \neq e^3$. Choice C is incorrect because $e^2 \neq e^{-3}$. Choice D is incorrect because $e^6 \neq e^5$.