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.