Use the properties of logarithms to write the expression as a single logarithm.

To combine an expression into a single logarithm using logarithm properties, you typically need an expression that involves multiple logarithms. Since your previous expression was incomplete, I'll illustrate how you can use the properties of logarithms to combine logarithmic expressions.

### Properties of Logarithms:
1. **Product Property**: \(\ln(a) + \ln(b) = \ln(a \cdot b)\)
2. **Quotient Property**: \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\)
3. **Power Property**: \(k \cdot \ln(a) = \ln(a^k)\)

### Example 1:
Suppose you have the expression:
\[
\ln(x) + \ln(y)
\]
Using the **Product Property**, this can be combined into a single logarithm:
\[
\ln(x \cdot y)
\]

### Example 2:
For a more complex expression like:
\[
2\ln(a) - \ln(b)
\]
You can first apply the **Power Property** to the first term:
\[
\ln(a^2) - \ln(b)
\]
Then, using the **Quotient Property**, you can combine them into a single logarithm:
\[
\ln\left(\frac{a^2}{b}\right)
\]

If you have a specific expression you need help with, feel free to provide it, and I can show you how to combine it into a single logarithm!

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**Here are 5 related questions to explore:**

1. How do you expand a logarithmic expression using logarithm properties?
2. What are the common mistakes to avoid when combining logarithmic expressions?
3. How do you solve logarithmic equations that require combining logarithms?
4. Can you explain the concept of logarithmic differentiation?
5. What are the applications of logarithmic properties in real-world problems?

**Tip:** Always ensure that the arguments inside the logarithms are positive when working with real numbers.

Learn how to combine logarithmic expressions into a single logarithm using logarithm properties. Explore examples and detailed explanations of the product property, quotient property, and power property of logarithms.

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