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The problem provided asks to **evaluate \( \ln(e^3) \)**.

### Solution:
We can use the logarithmic identity:

\[
\ln(e^x) = x \cdot \ln(e)
\]

Since \( \ln(e) = 1 \), the expression simplifies to:

\[
\ln(e^3) = 3 \cdot \ln(e) = 3 \cdot 1 = 3
\]

### Final Answer:
\[
\boxed{3}
\]

Would you like further details on this solution or have any follow-up questions?

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Here are 5 related questions to explore:

1. What is the general rule for \( \ln(a^b) \)?
2. How does the natural logarithm differ from logarithms with other bases?
3. Why does \( \ln(e) = 1 \)?
4. What are the properties of logarithms involving products and quotients?
5. How do logarithmic and exponential functions relate to each other?

**Tip:** Knowing basic logarithm properties can help simplify seemingly complex logarithmic expressions quickly!

Learn how to evaluate the natural logarithm ln(e^3) with a detailed step-by-step solution. This problem uses the key logarithmic property ln(e^x) = x * ln(e) and is suitable for high school students in Grades 10-12.

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