Choice A is the correct answer. Use properties of exponents.

1. Given: $e^{2x} = 50$.
2. Rewrite: $e^{2x} = (e^x)^2 = 50$.
3. Solve: $e^x = \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2} \approx 7.07$.

💡 Strategic Tip:$(a^m)^n = a^{mn}$, so $e^{2x} = (e^x)^2$.

Choice B is incorrect because$(e^x)^2 = 50$, not $e^x = 25$. Choice C is incorrect because this would give $e^{2x} = 10000$. Choice D is incorrect because$e^x eq e^{2x}$.