Set 6: Exponential Functions

Choice A is correct. Choice A is the correct answer. Use natural logarithm to solve. 1. Take natural log: $\ln(e^{3 x}) = \ln(8)$. 2. Simplify: $3x = \ln(8)$ (since $\ln(e^a) = a$). 3. Solve: $x = \frac{\ln(8)}{3}$. 4. Numerical: $\ln(8) \approx 2.079$, so $x \approx 0.693$. Strategic Tip: Natural log is the inverse of $e^x$: $\ln(e^x) = x$. Choice B is incorrect because this multiplies by 3 instead of dividing. Choice C is incorrect because logarithms are needed, not simple division. Choice D is incorrect because subtraction is wrong.