The natural logarithm of \( \frac{1}{4} \) can be simplified as follows:

\[
\ln \left( \frac{1}{4} \right) = \ln(1) - \ln(4)
\]

Since \( \ln(1) = 0 \), the equation becomes:

\[
\ln \left( \frac{1}{4} \right) = 0 - \ln(4) = -\ln(4)
\]

Thus, the solution is:

\[
\ln \left( \frac{1}{4} \right) = -\ln(4)
\]

Would you like more details or have any questions?

### Related Questions:
1. What is the value of \( \ln(4) \)?
2. How do you calculate logarithms using a calculator?
3. What is the relationship between natural logarithms and common logarithms?
4. Can logarithms of negative numbers be calculated?
5. How can you simplify other logarithmic expressions similar to \( \ln \left( \frac{1}{4} \right) \)?

### Tip:
Remember that \( \ln(a/b) = \ln(a) - \ln(b) \) is a useful property for simplifying logarithmic expressions involving fractions.

This guide explains how to simplify the natural logarithm ln(1/4) using key logarithmic properties. Learn step-by-step how the equation reduces to -ln(4), with a detailed breakdown of the formulas used. Suitable for Grades 10-12.

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