1. ln(x) = -2\n2. 3ln(x) = 6

Explanation:

Step1: Recall logarithmic - exponential relationship

The natural - logarithm function $\ln(x)$ is the inverse of the exponential function $y = e^{x}$. If $\ln(x)=y$, then $x = e^{y}$.

Step2: Solve $\ln(x)=-2$

Given $\ln(x)=-2$, by the relationship $x = e^{y}$, we have $x = e^{-2}=\frac{1}{e^{2}}$.

Step3: Solve $3\ln(x)=6$

First, divide both sides of the equation $3\ln(x)=6$ by 3. We get $\ln(x)=2$.

Step4: Apply logarithmic - exponential relationship again

Since $\ln(x)=2$, then $x = e^{2}$ by the relationship $x = e^{y}$.

Answer:

1. $x=\frac{1}{e^{2}}$
2. $x = e^{2}$