When it idles for a while and then you step on the gas blue smoke comes out of the tail pipe 2004 BMW X5 with 70k miles

fuel injectors. they are most likely pouring fuel into the cylinders instead of spraying a fine mist.

what kind of smoke by that I mean what colour is it and when does is happen under hard acceleration, at idle, when first started, under light acceleration, idling a long time? blue smoke is burning oil, white smoke is burning coolant sometimes accompanied with a sweet smell, black smoke its running rich. those are the basics.

check for clogged air filter and oxygen sensor if check eng light is on

Replaced the Idle Air Control?

Smoke from tail pipe or smoke from under hood?
A general rule of thumb if it is coming from tail pipe the color of smoke will tell you a lot.

White and thick means head gasket failure, Blue means oil is being burned.

I would recommend you check the seal of everything and make sure it is cleaned that had to do with vacuum or fuel distribution. EGR valve (gasket fails sometimes) IAC valve, MAP and MAF sensors, Fuel injectors, FPR (this will need replaced if leaking),

Also check you coolant and oil look for signs of either one mixing with one another, smell you coolant and make sure it don't smell like gas either, look around where the head meets the block and make sure you don't have any coolant leaking there. The smoke if from the tail pipe makes me think head gasket and these are simple checks. They are not 100% diagnosis but can lead you to the problem.

Also one obvious thing would be make sure no one put anything in your gas tank.

I would most likely look at the injectors first then the head gasket next.

you have the n62 engine in this x5 valve guide seals are leaking causing the blue smoke but i hate to tell you people havnt had much luck with repair in fact i am replacing the cylinder heads on a 750 with the same engine right now after an attempt to replace the valve guide seals failed to resolve the problem

Change PCV valves and are located on the lids of valves, when they are bad, so the car smokes just as you write. Here is a picture, price cca 20usd, replacing time: 5min does easy!!!!

A V8 engine will start to consume more oil as they get more and more
miles on them. The valve stem seals and piston rings wear, and let
more and more oil burn off in the exhaust. How many miles are you
travelling in said 3 weeks?

RINGS AROUN THE PISTON, OIL LEAKING INTO THE COMBUSTION CHAMBER

probably the oil rings on the pistons but might be one of the heads , not good either way