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Math Help - Binary

  1. #1
    Mad
    Mad is offline
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    Binary

    How many bits are needed to represent each integer?

    The only one I don't get is this one:

    3^1000

    How are you even supposed to figure that one up?

    The answer in the back of the book is 1585 but I don't know how to get it myself.
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  2. #2
    MHF Contributor
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    Which ones did you get?

    3^{1000}\;= \;2^{x}

    Solve for 'x'.

    It is not a difficult logarithm problem, but I'm not quite sure why 1 was not added to the result.

    4 = 2^{x} \implies x = 2, but 4_{10}\;=\;100_{2}, and that's clearly not 2 binary digits.
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