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Logarithmic Action (4)!

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. Please answer the questions that follow.

For any value c > 0, write 2 identities that express the relationships visually shown here.

Since logarithms are exponents, explain why (using what you already know about exponent properties), these two relationships must be true.