Logarithmic Action (3: V2)

Interact with the applet below for a few minutes. [br][b]At any time, you can move the LARGE BLACK POINT anywhere on the positive x-axis. [/b][br][br]Can you write an identity that expresses the relationship visually shown here? [br]How can we explain why this identity must be true?
Quick (Silent) Demo

Information: Logarithmic Action (3: V2)