A Visualization of Logarithms
Let , , , stand for the areas of the regions colored red, blue, orange, and green, respectively.[more]
In the right graphic, observe that . Moreover, , because:
Therefore the red area is .
In the case , the red area is .[less]
Reference: Füsun Akman, "Proofs without Words under the Magic Curve," The College Mathematics Journal, 33(1), 2002 pp. 42–46.