I think of a number and multiply it 1000 times by 4. The answer is the same as if I had started with twice the original number and multiplie

I think of a number and multiply it 1000 times by 4. The answer is the same as if I had started with twice the original number and multiplied it by 2 how many times?

$$\\x*4^{1000}=(2x)*2^y\\\\ x*2^{2000}=2x*2^y\\\\ x*2^{2000}=x*2^{y+1}\\\\ y=1999$$