Recent content by lucas7

  1. L

    Why is x^(1/x) = e^((1/x)lnx)?

    because x=ln(x1/x)... that was my first statement, should be correct for all x I think
  2. L

    Why is x^(1/x) = e^((1/x)lnx)?

    Look: x = ln b {e}^{x}=b {e}^{ln b}=b b={x}^{1/x} y=ln{x}^{1/x} {e}^{y} = {x}^{1/x} {e}^{ln{x}^{1/x}}={x}^{1/x} now a=x, b=1/x ln({a}^{b})=c ln({x}^{1/x}) = c {e}^{c}={x}^{1/x} {x}^{1/x}={e}^{ln{x}^{1/x}}
  3. L

    Why is x^(1/x) = e^((1/x)lnx)?

    x=ln({x}^{1/x}) so {e}^{x}={x}^{1/x} and {e}^{ln({x}^{1/x})}={x}^{1/x}
  4. L

    Why is x^(1/x) = e^((1/x)lnx)?

    I got it. But I fail to apply it for my case, when x has an exponential. Like {x}^{1/x}={e}^{(1/x)lnx}
  5. L

    Why is x^(1/x) = e^((1/x)lnx)?

    Do you know where can I find this theorem? I do not understand why one is equal to the otherI am doing some limits exercises and I came up with ({\frac{n+3}{n+1}})^{n} limit when n->infinity. And to calculate this limit wolphram alpha show this "formula" but I just can't understand. I have some...
  6. L

    Why is x^(1/x) = e^((1/x)lnx)?

    I know it is a very basic definition but that is it for me.
  7. L

    Why is x^(1/x) = e^((1/x)lnx)?

    I don't understand why.
  8. L

    Why is x^(1/x) = e^((1/x)lnx)?

    or why is ? thx in advance!
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