Hi there. First post to to forums, yay!
The pan law has to do with the fact, that when playing sound from 2 speakers at the same time, the sounds panned to middle will have a boost of about 6 decibels without compensation. The most common pan law is -3dB, which means things panned dead center will be boosted about 3 decibels.
It is a workflow thing and the pan law affects the way your stereo system fits your acoustics and how mono compatible your stereo mix will be. For example having a -6dB rule will play at the same level in mono as your stereo mix, because the center position level is compensated in full. -4.5dB law has been said to have been designed for very good, acoustically designed rooms and is closer to being totally mono-compatible. Most commonly this was used on old Solid State Logic consoles. The -3dB law is the most commonly used because it is a good compromise.
Some laws can be more suited for different listening/monitoring environments. It probably makes no big difference to the end product, but I have noticed that using a steeper pan law can make panning sound wider when mixing, because it automatically changes/compensates the level more.
I prefer -3 and -4.5 laws.
I’m not sure of the equal loudness though. I assume it uses some kind of a designed curve, but I’m not sure. Maybe it boosts the side and attenuates the center at the same time? Could it be doing +3dB compensation on sides and -3dB at center?
All the best,