Choice A is the correct answer. Equal bases means equal exponents.

1. Given: $e^{x+3} = e^{2x-1}$.
2. Equal bases: $x + 3 = 2x - 1$.
3. Solve: $3 + 1 = 2x - x$, 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$e^5 eq e^3$. Choice C is incorrect because$e^2 eq e^{-3}$. Choice D is incorrect because$e^6 eq e^5$.