Expanding the Super Roots/Logs

Multiplication is iterative addition. Exponentiation is iterative multiplication. Tetration is iterative exponentiation. Pentation is iterative tetration. Etc. These are all hyperoperations and there are infinity many of them. But these are only one third of the bigger picture.

I want to know more about the logarithms and the radicals of these operations and how to compute them. There are such thing as super roots and super logarithms, but from what I know they only apply to tetration. Also, I have only really found a way of computing the super square root, but that is not enough for me! ssrt(x)=eW(lnx)=lnxW(lnx)      (W() denotes the product log and ssrt() denotes the super square root)\text{ssrt}(x) = e^{W(\ln x)} = \frac{\ln x}{W(\ln x)} \; \; \; \bigg( W(\cdot ) \text{ denotes the product log and ssrt}(\cdot) \text{ denotes the super square root} \bigg)

What I want to know is how you would write these expanded super roots/logs and if there is any way to compute them?

Note by James Watson
3 months, 2 weeks ago

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@Gandoff Tan

Yajat Shamji - 3 months, 2 weeks ago

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