Dimesional analysis and tetration

[Chenjesu]

is there some use of tetration or superlog in dimensional analysis / metric units ?

In a physical model there would be extra constants like (ax)^(bx) that would cancel out the units in such a way that the result would still be meters or seconds on both sides. That's usually what happens. Dimensional analysis says that physically meaningful equations must be reducible to a dimensionless form.