How much damage do multiple projectile bows do?
Yes, each arrow does 10 damage so a 10x3 bow will do 30 damage per shot if they all hit (not including additional bonuses such as crit or elemental damage) and expend only one arrow.
There is one caveat that bomb arrow blast damage is capped for multi-shot bows so they aren't even more powerful than they already are.
Also in case you are wondering, the highest damage bow you can find in the game is:
A 32x5 Savage Lynel Bow for a whooping 160 damage per shot before bonuses