How many 12 volt batteries does it take to power a 3000 watt invertet for 24 hours?

You need 3000 x 24 watt-hours or 72,000 watt-hours. A typical car battery has a capacity of 50 Ah or 600 watt-hours, so you would need 120 car batteries, connected in the right combination of series and parallel to give the right voltage for the inverter.