### 2 videos in "Exponentials / Logarithms"

## The Natural Logarithm

The Natural Logarithm

3308 views, 3 ratings - 00:19:02

Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.

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The natural log function defined as the integral of 1/t dt.

- Table of Derivatives - Table of derivatives of several different functions.
- Derivatives and Integrals of exponential and natural logarithm functions - A list of derivatives and integrals of the exponential and natural logarithm function.

- What is the natural log function?
- What is ln?
- What are the properties of natural log?
- What is the integral of 1/x?
- What is the derivative of ln |x|?
- What is the integral of x^-1?
- What is the integral of du/u?
- What is the derivative of x^-x?

The natural log function is defined and explained, as well as its limits and properties. ln(xy) = ln x + ln y is proved in this video. A theorem is also given, explained and proven that the limit of ln x / x^r = 0 for any r > 0 as x goes to infinity. This is a very complete and interesting video on the natural logarithm.