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To calculate the IDF and TF-IDF values for the given words and documents:

1. **IDF (Inverse Document Frequency) for "machine"**:
   IDF is calculated using the formula:
   \[
   \text{IDF} = \log \left(\frac{N}{n_t}\right)
   \]
   where:
   - \( N \) is the total number of documents.
   - \( n_t \) is the number of documents containing the term.

   Given:
   - Total documents \( N = 10 \)
   - Documents containing "machine" \( n_t = 5 \)

   \[
   \text{IDF}_{\text{machine}} = \log \left(\frac{10}{5}\right) = \log(2) \approx 0.301
   \]

2. **TF-IDF (Term Frequency-Inverse Document Frequency) for "learning" in document d2**:
   TF-IDF is calculated using the formula:
   \[
   \text{TF-IDF} = \text{TF} \times \text{IDF}
   \]
   where TF (Term Frequency) is the number of times the term appears in the document.

   Given:
   - Term "learning" appears 8 times in document d2.
   - Documents containing "learning" \( n_t = 2 \)

   First, calculate the IDF for "learning":
   \[
   \text{IDF}_{\text{learning}} = \log \left(\frac{10}{2}\right) = \log(5) \approx 0.699
   \]

   Then, calculate the TF-IDF for "learning" in d2:
   \[
   \text{TF-IDF}_{\text{learning, d2}} = 8 \times 0.699 \approx 5.592
   \]

Would you like more details or have any questions?

Here are 5 numbered questions you can ask:

1. What is the importance of IDF in text analysis?
2. How do you calculate term frequency (TF)?
3. Can you explain more examples of TF-IDF calculation?
4. What are some applications of TF-IDF in real-world scenarios?
5. How does TF-IDF help in information retrieval?

**Tip:** Understanding the components of TF-IDF can significantly improve your ability to analyze and process textual data.

Explore IDF and TF-IDF calculations with detailed examples and formulas. Learn how these metrics are crucial in text analysis for understanding term importance across documents. Suitable for advanced learners and professionals.

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