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Math Help - solving e^x=5x+1

  1. #1
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    solving e^x=5x+1

    solving
    e^x=5x+1
    thanks
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  2. #2
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    Re: solving e^x=5x+1

    there is no exact solution for power-algebric equation
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  3. #3
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    Re: solving e^x=5x+1

    Quote Originally Posted by narjsingh View Post
    solving e^x=5x+1
    one solution determined by "observation" is ...

    x = 0

    the other solution can be approximated using technology ...

    x \approx 2.6603991
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  4. #4
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    Re: solving e^x=5x+1

    The non-evident root cannot be expressed analyticaly with the combination of a finite number of usual functions.
    It can be erxpressed with infinite series (complicated, not useful in practice)
    Usally, this kind of equation is solved thanks to numerical computation.
    The root can be expressed on a closed form thanks to the Lambert W function :
    x = -W(X) where X = -(exp(-1/5)-1)/5
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  5. #5
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    Re: solving e^x=5x+1

    Quote Originally Posted by skeeter View Post
    one solution determined by "observation" is ...

    x = 0

    the other solution can be approximated using technology ...

    x \approx 2.6603991
    In this case, It is ok, but in general it is diffecult to solve such equation directly
    for example : solve : e^x=x+2
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  6. #6
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    Re: solving e^x=5x+1

    Quote Originally Posted by Kyood View Post
    In this case, It is ok, but in general it is diffecult to solve such equation directly
    for example : solve : e^x=x+2
    solve exp(x)=x+2 for x - Wolfram|Alpha
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  7. #7
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    Re: solving e^x=5x+1

    Quote Originally Posted by Kyood View Post
    In this case, It is ok, but in general it is diffecult to solve such equation directly
    for example : solve : e^x=x+2
    I'm pleased that my solution meets your approval ... in "this case".
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  8. #8
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    Re: solving e^x=5x+1

    Very nice, skeeter,
    you used a special function W(x) which consedered as an approximate solutuion.
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  9. #9
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    Re: solving e^x=5x+1

    Quote Originally Posted by Kyood View Post
    Very nice, skeeter,
    you used a special function W(x) which consedered as an approximate solutuion.
    no ... I just solved e^x - 5x - 1 = 0 with a calculator.
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  10. #10
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    Re: solving e^x=5x+1

    \int_{0}^{\pi}\frac{x^{4}\left(1-x\right)^{4}}{1+x^{2}}dx =\frac{22}{7}-\pi <br />
    Last edited by divyaprashanth07; October 29th 2012 at 07:19 AM.
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  11. #11
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    Re: solving e^x=5x+1

    Quote Originally Posted by divyaprashanth07 View Post
    \int_{0}^{\pi}\frac{x^{4}\left(1-x\right)^{4}}{1+x^{2}}dx =\frac{22}{7}-\pi
    ... what does this incorrectly evaluated definite integral have to do with this thread?
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