## e^x and ln x

e^x and ln x
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### Meets NCTM Standards:

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.
Early Transcendental extra video lecture including exponentials and the natural logarithm.
• What is e?
• What is the limit definition of the number e?
• What are the properties of e^x?
• What is the derivative of e^x?
• What is ln x?
• How are e^x and ln x related?
• What are the properties of ln x?
• What is the change of base formula for logarithms and why does it work?
• What is logarithmic differentiation?
• What is the derivative of x^-x?
This video explains what the number e is, what the limit definition of e is, and what e^x looks like and acts like. Some really high-level proofs are explained in this video. These might be above the level of an ordinary Calculus student. The number e and the exponential function e^x are used to explain ln x, or log base e of x. Properties of logs are explained using rules of exponents.
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Reviewed by MathVids Staff on December 18, 2008.  