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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... loge is abbreviated to ln (read "lin") though Matlab uses log for this function. Thus, by definition y
= ex Replacing y in the second equation by ex we get
Replacing x in the first equation by ln x we obtain
It is common to write ex = exp(x). The functions ln and exp are inverses of one another. That is, they cancel each other out. Note ex
> 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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