It depends on what you are planning on running with the inverter.
The change from 12V to 110V is going to cause a change of about 10x the amps drawn from the battery.
This is a ball park example but it's close enough for planning;
Say you have a small device that would draw 300 watts when you plug it in at your home to the 110v outlet.
What that means is that the thing draws about 3 amps at 110 volts.
When you plug that same thing into the inverter, it will still draw 3 amps at 110volts from the inverter,
but your inverter is going to have to draw 10x the 3 amps or 30amps of 12 volt from your battery in order to give you the 300 watts.
You say the unit can give you 1500 watts?
Well if it did, it would draw more than 100 amps from your battery.
That's about the amps you might draw while cranking the starter.
How long do you want to do that?