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The question in the image asks for the transformation of the function \( f(x) = \log(x) \) when transformed into \( g(x) = 3 \log(x) \).

### Analysis:
The function \( f(x) = \log(x) \) is transformed into \( g(x) = 3 \log(x) \), which means that the logarithmic function is multiplied by a constant factor of 3.

This multiplication by 3 affects the vertical scaling of the graph of the function:
- **Stretch by a factor of 3**: This means that every output value of \( \log(x) \) is multiplied by 3, causing the graph to be stretched vertically by a factor of 3.

### Conclusion:
The correct transformation is **"Stretch by factor of 3."**

Would you like more details on logarithmic function transformations? Here are five related questions that expand on this topic:

1. What happens if \( f(x) = \log(x) \) is transformed to \( f(x) = \log(3x) \)?
2. How would \( f(x) = \log(x) \) change if transformed into \( f(x) = \log(x - 3) \)?
3. What is the effect of multiplying a logarithmic function by a negative constant, such as \( -3 \log(x) \)?
4. How does the graph of \( \log(x) \) compare to \( \log(x + 3) \) in terms of shifting?
5. Can you explain how vertical compression would affect a logarithmic function?

### Tip:
When analyzing transformations, remember that multiplication affects vertical scaling, while additions or subtractions within the argument affect horizontal shifts.

If f(x) = log(x), what is the transformation that occurs if g(x) = 3log(x)?

Understand the transformation of the logarithmic function f(x) = log(x) to g(x) = 3log(x). Learn how multiplying by 3 causes a vertical stretch. Ideal for high school students in Grades 9-12.

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