Nope....math lesson over.....sorry. You're in need of a GENERATOR, not an
inverter at this level of usage....It just makes more sense.

Larry, you've been beating that same dead horse for over 5 years and
you're still wrong. Yes, 3 KW continuous requires a generator, and
yes, 3 KW from an inverter requires a decent battery bank and heavy
cables. That doesn't mean that it isn't useful however. Lots of things
from microwave ovens, to electric tools, to hair dryers require high
power for relatively short periods of time, and that makes a high
powered inverter very useful to have on board.