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Proof of limit derivation of Natural Logrithm

  1. Apr 28, 2013 #1
    The natural logarithm can be expressed as
    lim n(x^(1/n)−1)
    n->ifinity

    Can someone please derive this for me? Ive tried using the limit definition of e^x and then applying f^-1(x) but i can only get
    ((n*x)-1)^1/n

    any help is greatly appreciated thanks!
     
  2. jcsd
  3. Apr 28, 2013 #2

    tiny-tim

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    hi cmcraes! :smile:

    (try using the X2 button just above the Reply box :wink:)

    x = elogx ? :smile:
     
  4. Apr 28, 2013 #3
    No that doesnt use limits nor does it prove anything other than the fact that the natural log and the exponential function cancel eachother out

    ps: im on mobile so its not easy to do math print
     
  5. Apr 28, 2013 #4

    tiny-tim

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    expand elogx/n :wink:
     
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