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Thread: solving e^x=5x+1

  1. October 28th 2012, 05:55 AM #1
    narjsingh
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    solving e^x=5x+1

    solving
    e^x=5x+1
    thanks
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  2. October 28th 2012, 06:12 AM #2
    Kyood
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    Re: solving e^x=5x+1

    there is no exact solution for power-algebric equation
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  3. October 28th 2012, 06:43 AM #3
    skeeter
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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. October 28th 2012, 07:59 AM #4
    JJacquelin
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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. October 28th 2012, 09:36 AM #5
    Kyood
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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. October 28th 2012, 10:27 AM #6
    JJacquelin
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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. October 28th 2012, 11:45 AM #7
    skeeter
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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. October 28th 2012, 12:41 PM #8
    Kyood
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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. October 28th 2012, 01:10 PM #9
    skeeter
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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. October 29th 2012, 06:28 AM #10
    divyaprashanth07
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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. October 29th 2012, 03:40 PM #11
    skeeter
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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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