1. **State the problem:** Simplify the expression $\frac{\ln(3x)}{3x}$. 2. **Recall the properties:** The expression is a fraction with a logarithm in the numerator and a product in the denominator. There is no direct simplification between $\ln(3x)$ and $3x$ since one is a logarithm and the other is a linear term. 3. **Rewrite the logarithm:** Using the logarithm property $\ln(ab) = \ln a + \ln b$, we have $$\frac{\ln(3x)}{3x} = \frac{\ln 3 + \ln x}{3x}.$$ 4. **Split the fraction:** $$= \frac{\ln 3}{3x} + \frac{\ln x}{3x}.$$ 5. **Final expression:** This is the simplest form unless further context or values for $x$ are given. **Answer:** $$\frac{\ln(3x)}{3x} = \frac{\ln 3}{3x} + \frac{\ln x}{3x}.$$