1. **State the problem:** Solve the equation $\ln(x) - \ln(3) = 2$ for $x$. 2. **Recall the logarithm property:** The difference of logarithms is the logarithm of a quotient: $$\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)$$ 3. **Apply the property:** $$\ln(x) - \ln(3) = \ln\left(\frac{x}{3}\right)$$ So the equation becomes: $$\ln\left(\frac{x}{3}\right) = 2$$ 4. **Rewrite the logarithmic equation in exponential form:** $$\frac{x}{3} = e^{2}$$ 5. **Solve for $x$:** $$x = 3e^{2}$$ 6. **Final answer:** $$\boxed{x = 3e^{2}}$$ This means $x$ is $3$ times the square of Euler's number $e$.