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Math Help - brain teaser

  1. #1
    Junior Member
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    Oct 2005
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    brain teaser

    given that 2^x = 1/square root of 2 and 2^y = 4(square of 2), find exact values of x and y.
    calculate the exact value of 2^y-x

    thanks..
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  2. #2
    Newbie
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    Oct 2005
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    Ok... because sqrt(n) = n^(1/2) and 1/(n^p) = n^(-p)
    2^x = sqrt(2)^(-1) = 2^(-1/2)
    so x = 1/2
    2^y=2^2=4
    so y = 2

    2^(x-y) = 2^(2-1/2) = 2^(3/2)
    and since n^(3/2) = sqrt(n^3), the final answer is sqrt(8) which is the same as 2*sqrt(2)
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  3. #3
    MHF Contributor
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    2^x = 1/sqrt(2)
    2^x = 1/ [2^(1/2)]
    2^x = 2^(-1/2)
    x = -1/2 or -0.5 -----------answer.

    2^y = 4sqrt(2)
    2^y = (2^2)[2^(1/2)]
    2^y = 2^(2 +1/2))
    2^y = 2^(5/2)
    y = 5/2 or 2.5 -----------answer.

    2^(y -x)
    = 2^(2.5 -(-0.5))
    = 2^(3.0)
    = 8 ---------------answer.
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  4. #4
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    Argh... stupid negatives
    Bah...
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