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

I discuss the history of the introduction of the natural logarithm and exponential functions, answering the question of how the logarithm was first discovered and how it's properties were derived, and also why it appeared when it did. I consider several other areas of inquiry that could have led to a theory of exponentials and logarithms, including: compound interest, population/economic/technological growth, physics, gambling, navigation, and pure mathematics. Then I explain the work of John Napier in constructing calculation tables for astronomers that introduced the natural log in 1614. 0:00 Intro 1:05 History of compound interest 6:55 Why exponential growth was not a recognized feature of life in the past 8:10 Exponential functions in physics 10:58 Exp and log in gambling 14:34 Navigation, meridional parts, and the integral of the secant 18:43 Calculation tables and Napier's introduction of ln(x) This is episode 6 in a series called Tricky Parts of Calculus, a series about the subtle and difficult parts