How people came up with the natural logarithm and the exponential function, So ME1

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