approximation of the log function
we can approximate for small :
A perhaps more interesting and useful result is that for small we have the approximation
In general, if is smaller than our approximation is practical. This occurs because for small , the area under the curve (which is what is a measurement of) is approximately that of a rectangle of height 1 and width .
Now when we combine this approximation with the formula , we can now approximate the logarithm of many positive numbers. In fact, scientific calculators use a (somewhat more precise) version of the same procedure.
For example, suppose we wanted . If we estimate by taking , we would be pretty close.
|Title||approximation of the log function|
|Date of creation||2013-03-22 15:18:38|
|Last modified on||2013-03-22 15:18:38|
|Last modified by||Mathprof (13753)|