https://file.aiquickdraw.com/mathbot/file/172735833164547z06x06.jpg

The image contains a mathematical expression involving logarithms. Here's the problem from the image:

\[
\text{Nilai }  \log 216 + 7 \log \frac{1}{49} = \ldots
\]

This translates to:

Find the value of \( \log 216 + 7 \log \frac{1}{49} \).

### Solution:

1. **Simplify the second term using logarithmic properties**:  
   \( \log \frac{1}{49} \) is the same as \( \log (49^{-1}) \). Using the logarithmic power rule:
   \[
   \log (49^{-1}) = -\log 49
   \]
   Therefore, the second term becomes:
   \[
   7 \log \frac{1}{49} = 7 (-\log 49) = -7 \log 49
   \]

2. **Now, the expression becomes**:
   \[
   \log 216 - 7 \log 49
   \]

3. **Simplify using logarithmic properties**:  
   Recall that \( \log a - b \log c \) can be rewritten as:
   \[
   \log \left(\frac{a}{c^b}\right)
   \]
   So, the expression simplifies to:
   \[
   \log \left(\frac{216}{49^7}\right)
   \]

This simplifies the problem into calculating \( \log \frac{216}{49^7} \). Since exact values require further calculation, you can approximate these using logarithm tables or a calculator.

Let me know if you would like to proceed with detailed steps for numerical evaluation or any clarification.

Would you like me to continue with approximations, or do you have any other questions?

### Related questions:
1. What is the general power rule for logarithms?
2. How do we simplify expressions with multiple logarithmic terms?
3. What are common logarithmic identities useful for simplifying complex logarithms?
4. How can we express a logarithm of a fraction using properties of logs?
5. How does changing the base of a logarithm affect the simplification?

### Tip:
Always remember the basic logarithmic rules like the power rule, product rule, and quotient rule to simplify complex logarithmic expressions efficiently.

Learn how to simplify the logarithmic expression log 216 + 7 log (1/49) using basic logarithmic properties. This problem involves the power rule and quotient rule of logarithms, making it suitable for students in Grades 10-12.

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