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Logarithmic Action (3)!

Author:
Tim Brzezinski
Topic:
Logarithm, Logarithmic Functions
Interact with the applet below for a few minutes. At any time, you can move the purple point with coordinates (c, 0) anywhere on the positive x-axis. For any value c > 0, can you write an identity that expresses the relationship visually shown here? Algebraically show why this identity must be true for all values c > 0.

Quick (Silent) Demo

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