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.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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4.08%

step-by-step explanation: