Sorry but no.
Absolutely no one cares about the mathematical purity of a unit like the decibel. It's a hammer that turns log stuff into easy to work with linear stuff. It's x10 because that turns into reasonably easy to use numbers with enough precision to use casually. Otherwise it's just a log ratio. Any suffix is a log ratio to a reference value for the entire system (dBv / dBm etc).
Say in a 50 ohm system I have an level 7 mixer then I need 7dBm into the port. My oscillator kicks out 0dBm (1mW). Then I need a 7dB gain block. I go to the datasheet for the MMIC and pick out a bias network that gives me around 7dB. I grab a eval board for the MMIC, solder the resistors on it, shove this on my VNA and throw 0dBm in one end and see if 7dBm comes out of the other end at the frequency I need.
It's like Laplace. Do you really want to spend hours doing calculus?
Source: actual electrical engineer, not some clueless hobby blogger. I really wish people would stop writing authoritative sounding articles on stuff they clearly have little experience with.