A Visualization of Logarithms

Let , , , stand for the areas of the regions colored red, blue, orange, and green, respectively.
In the right graphic, observe that . Moreover, , because:
and .
Therefore the red area is .
In the case , the red area is .


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Reference: Füsun Akman, "Proofs without Words under the Magic Curve," The College Mathematics Journal, 33(1), 2002 pp. 42–46.


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