1. **State the problem:** Solve the equation $\ln x = -3$ for $x$. 2. **Recall the definition of natural logarithm:** The natural logarithm $\ln x$ is the inverse function of the exponential function $e^x$. This means if $\ln x = y$, then $x = e^y$. 3. **Apply the inverse operation:** Given $\ln x = -3$, we exponentiate both sides with base $e$ to isolate $x$: $$x = e^{-3}$$ 4. **Interpret the result:** The value $e^{-3}$ is a positive number since the exponential function is always positive. 5. **Final answer:** $$\boxed{x = e^{-3}}$$