The expression \( \ln\left(e\right) \) simplifies as follows:

\[
\ln(e) = 1
\]

This is because the natural logarithm \( \ln(x) \) is the inverse function of the exponential function \( e^x \), meaning:

\[
\ln(e^1) = 1
\]

Would you like further details on logarithmic properties or any related concepts?

Here are 5 related questions you might explore:
1. What is the general definition of the natural logarithm?
2. How does \( \ln(a^b) \) simplify using logarithmic rules?
3. What is the derivative of \( \ln(x) \)?
4. How does the change of base formula for logarithms work?
5. Can you simplify \( \ln(e^x) \)?

**Tip:** Remember that logarithms are the inverse of exponentiation, which helps simplify many complex expressions.

Explore how to simplify the natural logarithm of e, \ln(e). This problem demonstrates the inverse relationship between logarithmic and exponential functions, simplifying \ln(e) to 1. Suitable for high school students in Grades 10-12.

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