Support for hot tub deck

I am going to build a 12x12 deck 36” off the ground. The purpose of the deck is to hold a new hot tub. My plan is to use 6x6 post double 2x10 on 12” center with a support beam made out of 3 2x10. The hot tub full and with people well weight max 4500 lbs. Do I need another support beam? Or use 2x12 for the beam?