For trips of about a week, most people can take enough clothes with them to avoid excess baggage fees on the flight.
For longer than that, you either use the astoundingly expensive hotel laundry service, or a bottle of dhobi-gloop and the room bath. Than wait days for your clothes to dry....
For 3 weeks, it would be a bit much to rely on having to use dhobi-gloop - and the laundry charges would be somewhat excessive. So a
reasonable combination of both methods would seem the way to go. Socks, underwear, most shirts - dhobi-gloop. Other stuff - laundry.
Sometimes it's almost cheaper to find the nearest store and but some new socks etc than it is to get your own laundered.....