The Natural Logarithm
The 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 ln y = x
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.
> 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.