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One more curve without name:
Hmmm - that curve looks familiar 😉
a is about 2 and b approx 12 in that drawing.
The binary log of 12 sure is not 100 - not even close.
BTW - you really should forget abou those "units" in power functions, logarithms!
It really does not make sense.
What do you think is log (8m, 2m) ? Could it be 3= No! Because (2m)^3 = 8 m^3 and not 8 m.
So can we say that log(8m^3, 2m)=3? Probably, but you would have to use the "result" of the calculation as exponent of the first argument. This really is nothing useful!
WE