The expression $\ln(x)$ refers to the natural logarithm of $x$, which is the logarithm to the base $e$, where $e$ is Euler's number, approximately equal to 2.718. The natural logarithm is the inverse of the exponential function $e^x$.

To solve an equation involving $\ln(x)$, you would typically need to:

1. Isolate $\ln(x)$ on one side of the equation if it's part of a larger expression.
2. Exponentiate both sides to remove the logarithm. This involves raising both sides to the base $e$, since the inverse of $\ln(x)$ is $e^x$.

For example:

• If you have $\ln(x) = 2$, to solve for $x$, you would exponentiate both sides: $e^{\ln(x)} = e^2$ Since $e^{\ln(x)} = x$, this simplifies to: $x = e^2$ Therefore, $x \approx 7.389$.

Would you like a more specific example or further clarification on solving logarithmic equations?

Here are 5 questions that might expand on this topic:

1. What happens if the equation has an additional constant, like $\ln(x) + 3 = 5$?
2. How do you solve logarithmic equations with different bases (e.g., $\log_2(x)$)?
3. What are the properties of the natural logarithm?
4. How do you differentiate or integrate functions involving $\ln(x)$?
5. What does the graph of $\ln(x)$ look like, and how can you interpret it?

Tip: Always remember that the domain of $\ln(x)$ is $x > 0$, because the logarithm of a non-positive number is undefined in real numbers.