I do not know any 100ah hour that can supply enough current for an A/C or microwave operation. If you are going to use a 3,000 watt inverter, you are going to need about 250A of current to operate that at full tilt.
A real crude way of figuring it out would be that 1,500watt microwave would need 150A to operate. Which 100ah battery can do that? Same with A/C.
Define evening? From 5pm-10pm? I highly doubt if you will run a microwave for 5 hours. But if you did, you would need about 9000watts of power. A 100ah battery has about 1,200watts. So, you would need about 7.5 100ah batteries. If you plan on running A/C at the same time, you would need another 7.5 100ah batteries. So, you would need 15 100 ah batteries. Using Battle Born currency, that would be about $15,000 [including WA State sales tax]. If you wait for their sale......... Naw, lets not derail this thread
Not certain how much a TV runs, but maybe another 100ah battery will supply the juice to keep the TV working for 5 hours.
If you think solar panels will supply that type of current, they can, but you will need a lot of them and at night that's probably not going to happen. There are plenty of members here that have real data that can shed some light on solar power generation.
The way I think is, solar keeps the batteries charged. It has nothing to do with running your A/C, microwave, and TV. That is what the batteries do. Before anyone has a cow, yes solar does supply all the electrons the consumer will use, but typically most people use batteries to buffer the current draw, not the solar panels. I hope that makes sense because it certainly does not seem to be coming out right.
Feel free to question my numbers. I did not use a calculator, I did not consider efficiency loss either. Heck....I'm probably way off base, you just can't trust an automotive mechanic these days.