


LogarithmsThe Natural LogarithmThe common logarithm is used in many scientific applications, such as the Richter scale. In mathematics, the most commonly used base for logarithms is the number e = 2.718281828... log_{e} is abbreviated to ln (read "lin") though Matlab uses log for this function. Thus, by definition y = e^{x} ln y = x Replacing y in the second equation by e^{x} we get
Replacing x in the first equation by ln x we obtain
It is common to write e^{x} = exp(x). The functions ln and exp are inverses of one another. That is, they cancel each other out. Note e^{x}
> 0 for any x. Here are the graphs of ln and exp:
Each graph is a reflection of the other with respect to the line y = x.
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