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The expression shown is \(\ln\left(\frac{V}{W}\right)\). To expand this logarithmic expression, we can use the **logarithm quotient rule**:

\[
\ln\left(\frac{a}{b}\right) = \ln(a) - \ln(b)
\]

Applying this rule to \(\ln\left(\frac{V}{W}\right)\), we get:

\[
\ln\left(\frac{V}{W}\right) = \ln(V) - \ln(W)
\]

This is the expanded form of the given logarithmic expression.

Would you like more details or have any questions?

Here are five related questions to further explore this concept:
1. How would you expand \(\ln\left(\frac{x^2}{y^3}\right)\)?
2. What is the expansion for \(\ln\left(\frac{a \cdot b}{c}\right)\)?
3. How do you simplify \(\ln(a^2 b)\) using logarithmic rules?
4. Can you apply the logarithm properties to simplify \(\ln\left(\frac{\sqrt{x}}{y}\right)\)?
5. What are the conditions for logarithms to be well-defined?

**Tip:** Remember, when dealing with logarithms, all arguments inside the logarithms must be positive for the expressions to be valid!

Expand the logarithm ln(V/W). Assume all expressions exist and are well-defined.

Learn how to expand the logarithmic expression ln(V/W) using the quotient rule of logarithms. This step-by-step solution covers key logarithmic concepts and is suitable for high school students in Grades 9-12.

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