FINAL ANSWER:
The value of k (the stretch factor) is 100.
Steps to Solve:
Analyze the Original Graph:
y = log_10(x) has a characteristic shape with the y-intercept at (1, 0).
Translate 2 Units Up:
The new equation becomes y = log_10(x) + 2, shifting the y-intercept to (1, 2).
Determine Equivalent Stretch Factor:
To achieve the same y-value of 2 at x = 1 using a stretch, we need a factor that "slows down" the original graph's growth.
This means stretching it horizontally, making it wider.
The correct stretch factor is 10^2 = 100.
FINAL ANSWER:
The value of k (the stretch factor) is 100.
The probable question is in the image attached.