2008 Toyota Sienna consuming oil

The problem is its drinking oil, there is no residue on tail pipe and it is not leaking, Toyota is giving me the runaround, at about 2000 mile there was no oil in it, I put 3 1/2 Qs in it then at 3400 miles I got an oil change, 3631 miles I took it to toyota it was at the full mark, at 4921 it had drank 1/2 Q toyota told me to drive it some more, at 5589 it had drank 1.1Q toyota filled the oil to the full mark and at 6526 miles I'm down another 1/2 Q, toyota technician says there is no leak and its not buning it cause there is no oil residue in tail pipe. All I want to know is if there is no leak and no residue where is the oil going.