You have the function \( y(x) = \ln \left( \frac{1}{2} \right) \).

Since \( \ln \left( \frac{1}{2} \right) \) is a constant (not dependent on \(x\)), you can simplify this:

\[
y(x) = \ln \left( \frac{1}{2} \right) = \ln (1) - \ln (2) = 0 - \ln (2) = -\ln (2)
\]

Thus, the function becomes:

\[
y(x) = -\ln (2)
\]

This means that for any value of \(x\), \(y(x)\) remains constant as \(-\ln(2)\).

Would you like more details or have any questions?

Here are some related questions:

1. What is the value of \(\ln(2)\)?
2. How do you differentiate a logarithmic function?
3. What is the graphical interpretation of constant functions?
4. Can we generalize the logarithmic properties for any other fractions?
5. How do you solve equations involving natural logarithms?

**Tip**: The natural logarithm, \(\ln(x)\), is the inverse of the exponential function \(e^x\). Understanding this relationship can be very helpful in solving logarithmic equations.

Explore the function y(x) = ln(1/2), its simplification using logarithmic properties, and why it represents a constant value of -ln(2). Learn how to work with logarithmic functions and understand constant functions. Suitable for students in Grades 10-12.

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