1. **State the problem:** Solve the equation $e^{3x} = 12$ for $x$. 2. **Recall the formula and rules:** To solve equations involving exponentials, we use the natural logarithm $\ln$ because it is the inverse of the exponential function $e^x$. Applying $\ln$ to both sides helps us isolate the variable. 3. **Apply the natural logarithm to both sides:** $$\ln\left(e^{3x}\right) = \ln(12)$$ 4. **Use the logarithm power rule:** $$3x \cdot \ln(e) = \ln(12)$$ Since $\ln(e) = 1$, this simplifies to: $$3x = \ln(12)$$ 5. **Solve for $x$ by dividing both sides by 3:** $$x = \frac{\ln(12)}{3}$$ 6. **Final answer:** $$x = \frac{\ln(12)}{3}$$ This is the exact solution. You can approximate $\ln(12) \approx 2.4849$, so: $$x \approx \frac{2.4849}{3} \approx 0.8283$$