Set 3: Exponential Functions (Intermediate)

Choice A is correct. Choice A is the correct answer. Use the definition of natural logarithm. 1. Definition: $\ln(x) = y$ means $e^y = x$. 2. Apply: $\ln(x) = 2$ means $x = e^2$. 3. Calculate: $e^2 \approx 7.389$. Strategic Tip: $\ln$ and $e^x$ are inverse functions: $e^{\ln(x)} = x$ and $\ln(e^x) = x$. Choice B is incorrect because this confuses the input and output. Choice C is incorrect because this inverts incorrectly. Choice D is incorrect because this is $e^1$, not $e^2$.