How people came up with the natural logarithm and the exponential function #SoME1

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Reconstructs how Napier, Bürgi, Saint-Vincent and Euler arrived at logarithms and the exponential, from computation tables to areas under the hyperbola, a #SoME1 entry by a research mathematician who stresses rigour.

How mathematicians historically arrived at the natural logarithm and the exponential function.

Video by Daniel Rubin, played through YouTube's embedded player.