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Thread: how this is derived

  1. #1 how this is derived 
    Forum Freshman
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    Jun 2005
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    hello:

    how is this derived:
    x^(1/x)=e^(ln(x)/x)

    any tip is appreciated


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  3. #2 Re: how this is derived 
    Moderator Moderator
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    Quote Originally Posted by kreidxkj
    hello:

    how is this derived:
    x^(1/x)=e^(ln(x)/x)

    any tip is appreciated
    By the law of logs and of indices.

    If e<sup>ln(x)/x</sup> = x<sup>1/x</sup>

    then lnx<sup>1/x</sup> = (lnx)/x = 1/x(lnx) = lnx<sup>1/x</sup>.
    As desired.

    Oh. That's the proof, and you asked for the derivation. Ok, set
    e<sup>ln(x)/x</sup> = y

    then ln(y) = ln(x)/x and ask what is y, following the steps above.


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  4. #3 thanks,i get it 
    Forum Freshman
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    Jun 2005
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    thanks:

    i suddenly know it is just that simple after i get your answer.
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