Question 707608
I would say the units for log(x) deserve a new name, because you cannot add the value of log(x) to lengths in meters, just as you cannot add any quantity in any other unit to lengths in meters. You could call it log-meter.
However, I have never heard of a name for such a unit.
The only logs that "sort of" got a name are
1 unit of pH = -log(1 mole of hydrogen ion per liter)
and decibels.
They are not exactly logs, but they involve logs.