1. **State the problem:** Solve for $x$ in the equation $$4x = 3 \ln 0.0069$$. 2. **Recall the properties:** The natural logarithm function $\ln$ is the inverse of the exponential function $e^x$. 3. **Isolate $x$:** Divide both sides of the equation by 4 to solve for $x$: $$x = \frac{3 \ln 0.0069}{4}$$ 4. **Intermediate step showing cancellation:** $$x = \frac{\cancel{4} \times \frac{3}{\cancel{4}} \ln 0.0069}{1} = \frac{3}{4} \ln 0.0069$$ 5. **Calculate $\ln 0.0069$:** Using a calculator, $$\ln 0.0069 \approx -4.9767$$ 6. **Substitute and simplify:** $$x = \frac{3}{4} \times (-4.9767) = -3.7325$$ 7. **Final answer:** $$\boxed{x \approx -3.73}$$