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Math Help - Please help point out the error

  1. #1
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    Please help point out the error

    The following can't be true, but I can't discover my error. Can anyone see it?

     <br />
\frac{i \pi n}{x}=\ln(-1^{\frac{n}{x}})=\ln(-1)+\ln(1^{\frac{n}{x}})=i\pi<br />

    (n is a positive integer and x is a positive real number)


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  2. #2
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    Don't you think this is a topic for university math help?^^
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  3. #3
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    Quote Originally Posted by rainer View Post
    The following can't be true, but I can't discover my error. Can anyone see it?

     <br />
\frac{i \pi n}{x}=\ln(-1^{\frac{n}{x}})=\ln(-1)+\ln(1^{\frac{n}{x}})=i\pi<br />

    (n is a positive integer and x is a positive real number)


    Thanks
    (-1)^{\frac{n}{x}}=(-1)(-1)....(-1) for \frac{n}{x} times

    or \left(\sqrt{-1}\right)^{\frac{2n}{x}}

    Using the laws of logs.. log(ab)=loga+logb

    but you cannot split (-1)^{\frac{n}{x} into (-1)(1)^{\frac{n}{x}}
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