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.