help pls!! How many different numbers between 1/1000 and 1000 can be written either as a power of 2 or as a power of 3, where the exp

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help pls!!
How many different numbers between 1/1000 and 1000 can be written either as a power of 2 or as a power of 3, where the exponent is an integer? Remember that we’re counting all possible numbers, not just integers.

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Vân Khánh 2 months 2021-07-31T07:36:55+00:00 1 Answers 0 views 0

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    2021-07-31T07:37:56+00:00

    How many different numbers between 1/1000 and 1000 can be written either as a power of 2 or as a power of 3, where the exponent is an integer?

     

    2^9 = 512    So that is  9+9+1 = 19 powers of 2

    3^6=729     so that is 6+6+1 = 13 powers of 3

     

    Now you just have to work out how many are powers of 2 and 3 because they have  been counted twice.

     

    If they are powers of 2 and 3 that means they are powers of 6

    6^3 = 216 which is the biggest so that is  3+1+3 = 9

     

    So I think the answer is      19+13-9 = 23

    mark me as a brill please

     

     

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