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The 5 points plotted below are on the graph of y = b^x. Based only on these 5 points, plot the 5 corresponding points that must be on the graph of y= log_b x.

User Shushan
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1 Answer

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The plot of the 5 corresponding points are plotted and attached

how to find the points

The given set of points on the graph of y = ㏒_b x corresponds to the inverse relationship with the function y = bˣ.

The key observation is that each point on the graph of y = bˣ can be reflected across the line y = x to find a corresponding point on the graph of y = ㏒_b x.

This creates the effect of interchanging the variables. This is solved below. The the points be A B C D E

A (0, 1) → (1, 0)

B (1, 2) → (2, 1)

C (2, 4) → (4, 2)

D (3, 8) → (8, 3)

E (4, 16) → (16, 4)

The 5 points plotted below are on the graph of y = b^x. Based only on these 5 points-example-1
The 5 points plotted below are on the graph of y = b^x. Based only on these 5 points-example-2
User Yigal
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