Whenever you are looking for an oil consumption problem, you start by changing the oil, logging the miles and checking the dipstick weekly. DO NOT add oil unless the level is AT OR BELOW the add mark. All engines use oil, some more than others and 90% of all engines are MORE than a quart low at 3k miles. That would mean that at around 2000-2500 miles, they were a quart low.
The MINIMUM level of usage is a quart every 750 miles, according to all the car makers. While that would be totally unacceptable for a new car, that is where we start planning the overhaul of an older engine.
Once you verify that you are using more than a quart every 1500 miles or less and you know you don't have an external oil leak, you would begin by pulling the spark plugs which will tell you which cylinder(s) is burning the oil. By performing a leak down test and a wet / dry test will then tell you if it is a piston ring or valve guide or seal problem. If your oil level is still above the add mark at 1500-2000 miles, everything is fine.
Piston ring problem --- No choice but to either wait it out or fix it by overhauling or replacing the engine. Cost will vary between $1500-4000 depending on the engine size.
Valve guides or seals --- IF you have a puff of blue or grey smoke from the tailpipe in the morning, IF you don't have any other smoke throughout the day, IF you have a very minor oil usage problem, IF you have between 60k to 100k on the old clock (speedo), all of that points to bad valve guides or seals. My advice is never fix this very expensive repair UNTIL you begin to use a lot of oil AND oil foul your spark plugs. Often you will have this "puff of blue or grey smoke first thing in the morning and never again during the day" for years before you foul your first spark plug.
You see, no one can be sure if your oil consumption problems are because of bad valve guides or seals. The seals typically cost $200-500 depending on the engine but to pull the heads and rebuild them will cost $850-1500. So what happens if they think it's bad seals and do all the work to replace them, and that doesn't fix your oil consumption problem? All of that money was wasted and you still have the same problem.