Quote:
Originally Posted by Raman
That website http://wims.unice.fr 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.
Quote:
Originally Posted by Raman
I had faced a problem which asked me to give an algorithm to check out if N is a perfect power, x ^{y} where that value of y is ≥ 2. I told that it can be done by using checks of , , , , , , ... alternately, what value to check upto for base? Till N = z ^{z}, 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.