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Show that ln(e)=1.

  1. Nov 8, 2009 #1
    1. The problem statement, all variables and given/known data
    Show that ln(e)=1.


    2. Relevant equations
    ln(x)=antiderivative from 1 to x of dt/t


    3. The attempt at a solution
    I assume we have to use the fact that e= lim as n->infinity of (1+1/n)^n, and perhaps can apply l'Hopital's rule to transform that limit -- but I'm not sure where to go from there.
     
  2. jcsd
  3. Nov 8, 2009 #2

    jgens

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    Gold Member

    If [itex]e = \lim_{n \to \infty}(1 + \frac{1}{n})^n[/itex], then we know that [itex]ln(e) = \lim_{n \to \infty}(n)ln(1 + \frac{1}{n})[/itex]. Now put this in a form where you can apply L'Hospital's Rule.
     
  4. Nov 8, 2009 #3
    Ah, I see! Thank you.
     
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