1. **State the problem:** Solve the equation $y = \ln(3x)$ for $x$. 2. **Recall the definition of the natural logarithm:** The natural logarithm function $\ln(a)$ is the inverse of the exponential function $e^a$. This means if $y = \ln(a)$, then $e^y = a$. 3. **Apply the inverse operation:** Given $y = \ln(3x)$, exponentiate both sides to remove the logarithm: $$e^y = e^{\ln(3x)}$$ Since $e^{\ln(3x)} = 3x$, we have: $$e^y = 3x$$ 4. **Solve for $x$:** $$x = \frac{e^y}{3}$$ 5. **Important domain note:** Since the argument of the logarithm must be positive, $3x > 0 \Rightarrow x > 0$. **Final answer:** $$x = \frac{e^y}{3}$$