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Math Help - The equation

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    The equation

    The equation

     x^x=1

    has the obvious solution x=1 find others
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by perash View Post
    The equation

     x^x=1

    has the obvious solution x=1 find others
    As the graph shows, the only other possible solution is x = 0. But as 0^0 is not defined, it can't be 1. Thus there are no other solutions.

    -Dan
    Attached Thumbnails Attached Thumbnails The equation-exponential.jpg  
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  3. #3
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    Quote Originally Posted by topsquark View Post
    As the graph shows, the only other possible solution is x = 0. But as 0^0 is not defined, it can't be 1. Thus there are no other solutions.

    -Dan
    Alternatively, x^x = 1 \Rightarrow x \ln x = 0.

    Therefore x = 1 or x = 0. But as topsquark has quite rightly pointed out .......

    Note however that \lim_{x \rightarrow 0} x^x = 1 ......
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