Abstract
The entire algebra of logarithm is based on the following definition: The logarithm of a number a to the base b is a number c such that a can be expressed as b to the power c.
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Notes
- 1.
Swiss mathematician Euler (pronounced “Oiler”) introduced the natural logarithm. If you wonder why the symbol for ‘natural logarithm’ is not ‘nl’, just remember that for the French speaking mathematician it was “le logarithm natural”. In which case, ‘ln’ makes sense.
- 2.
For a detail discussion of measures of estimation accuracy, see the Appendix to Chap. 11.
- 3.
This problem is taken from Functions Modeling Change by Connaly et al. 2004 John Wiley and Sons. The data is originally from the Recording Industry Association of America, Inc., 1998.
- 4.
Try this on your calculator. Start by \(n = 10\), change it to 100, then 1000, 10000, and 100000. You’ll see that the value of \(\left( 1 + \frac{1}{n}\right) ^n\) goes from 2.59374 to 2.70481, 2.71692, 2.71814, and 2.71826. Number \(e\) to 5 decimal places is 2.71828. It is clear that larger \(n\) becomes closer the result gets to \(e\).
- 5.
As before, I am using the designation natural for exponential function to the base \(e\).
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Vali, S. (2014). Logarithmic and Exponential Functions. In: Principles of Mathematical Economics. Mathematics Textbooks for Science and Engineering, vol 3. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-036-2_9
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DOI: https://doi.org/10.2991/978-94-6239-036-2_9
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