1. The problem is to solve the equation $\ln x = -2$ for $x$. 2. Recall that the natural logarithm function $\ln x$ is the inverse of the exponential function $e^x$. 3. To solve for $x$, rewrite the equation in exponential form: $$x = e^{-2}$$ 4. This means $x$ is the number which, when you take the natural logarithm, gives $-2$. 5. The exact solution is: $$x = e^{-2}$$ 6. Numerically, $e^{-2} \approx 0.1353$. Therefore, the solution to $\ln x = -2$ is $x = e^{-2} \approx 0.1353$.