The expression you provided is \( \ln\left(e^{1/3}\right) \).

Using the property of logarithms, \( \ln(a^b) = b \cdot \ln(a) \), we can simplify this expression.

\[
\ln\left(e^{1/3}\right) = \frac{1}{3} \cdot \ln(e)
\]

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

\[
\frac{1}{3} \times 1 = \frac{1}{3}
\]

So, \( \ln\left(e^{1/3}\right) = \frac{1}{3} \).

Would you like more details on logarithmic properties or have any other questions?

Here are 5 related questions:
1. How would you simplify \( \ln\left(e^2\right) \)?
2. What is the value of \( \ln(e^x) \) for any real number \( x \)?
3. How can you use logarithm properties to solve \( \ln\left(a^b\right) \)?
4. What is the derivative of \( \ln\left(e^x\right) \) with respect to \( x \)?
5. How does the natural logarithm function behave as \( x \) approaches infinity?

**Tip:** The natural logarithm \( \ln(x) \) is the inverse function of the exponential function \( e^x \).

Learn how to simplify ln(e^(1/3)) using logarithmic properties and the natural logarithm. Understand the relationship between logarithms and exponential functions with a clear explanation. Suitable for high school students studying advanced algebra and calculus.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation