A Visualization of Logarithms

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Let , , , stand for the areas of the regions colored red, blue, orange, and green, respectively.

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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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Contributed by: Soledad Mª Sáez Martínez and Félix Martínez de la Rosa (March 2011)
Open content licensed under CC BY-NC-SA


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Details

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



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