To solve the equation $3\ln(x) - 2 = 0$ for $x$, follow these steps:

1. Isolate the logarithm: $3\ln(x) = 2$

2. Divide both sides by 3: $\ln(x) = \frac{2}{3}$

3. Exponentiate both sides to get rid of the natural logarithm (since $\ln(x)$ is the natural logarithm, the base of the exponentiation is $e$): $x = e^{\frac{2}{3}}$

So, the exact solution is: $x = e^{\frac{2}{3}}$

Would you like any details or have any questions about this solution?

Here are five related questions you might find interesting:

1. How would you solve $4\ln(x) + 1 = 0$?
2. What is the approximate value of $e^{\frac{2}{3}}$?
3. Can you solve $5\ln(x) = 3\ln(2)$?
4. How would you solve $\ln(x^2) = 4$?
5. What happens if you take the logarithm of both sides of the equation $x^3 = 10$?

Tip: Remember that $\ln(x)$ is only defined for $x > 0$, so when solving logarithmic equations, always check that your solutions are positive.