Assume the base is 10.
x^y = log x
log x^y = log log x
y log x = log log x
∴ y = (log log x)/log x
Not sure if this is the correct forum, but I was wondering if a log transformation can be expressed in terms of a power transformation. That is, can you take the implicit function x^y=log(x) and make it explicit by solving for y?
I mean I can solve for y easily but the result isn't satisfactory because it still includes the "log(x)" function, so you'd have an infinitely nested part of the equation if you keep substituting log(x) with x^y.
Yes, I can see that, but you still have log(x) in the equation. So if you were to express a log transformation strictly as a power transformation would it not be impossible? You would still have to take the log of x in order to do so which defeats the whole purpose of such a conversion. I guess I answered my own question. Sorry