What are the powers of 4 through 1000

{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}

Step-by-step 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.

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step-by-step explanation: