View Single Post
Old 2011-04-13, 19:17   #2
CRGreathouse's Avatar
Aug 2006

3·1,987 Posts

Originally Posted by Raman View Post
That website contains a plenty of useful online calculators,
really a lot, but I couldn't find out a place where inverse of functions is being sought.
The problem is hard and in general cannot be done symbolically.

Originally Posted by Raman View Post
I had faced a problem which asked me to give an algorithm to check out if N is a perfect power, xy where that value of y is ≥ 2. I told that it can be done by using checks of \sqrt{x}, log_2(x), ^3\sqrt{x}, log_3(x), ^4\sqrt{x}, log_4(x), ... alternately, what value to check upto for base? Till N = zz, for some value of z. Thus, how to write up with that value of z as a function of N? How does that way work out rather...
For that one you'll need a special function like Lambert's W, or numerical techniques. I think it's exp(W(log N)). W(x) is about log x - log log x, so this is roughly exp(log log N - log log log N) = log N / log log N, where log is the natural log.

Last fiddled with by CRGreathouse on 2011-04-13 at 19:20
CRGreathouse is offline   Reply With Quote