Answer:
{4^0, 4^1, 4^2, 4^3, 4^4}, or, with a bit of rounding off,
{4^0, 4^1, 4^2, 4^3, 4^4, 4^5} = {1, 4, 16, 64, 256, 1024}
Explanation:
I wanted to determine the largest power of 4 that does not exceed 1000. Here's what I did:
4^x = 1000. Taking the ln of both sides, we get x ln 4 = ln 1000.
6.9078
Solving for x: x = --------------- = 4.98
1.3863
Thus, the answer to this question is {4^0, 4^1, 4^2, 4^3, 4^4}. If you're willing to talk in terms of approximations, then there'd be one more power of 4 in this set: 4^5. Note that 4^5 = 1024, whidh is just a bit over 1000.