Results 1 to 3 of 3

Thread: Solve in R

  1. #1
    Super Member dhiab's Avatar
    Joined
    May 2009
    From
    ALGERIA
    Posts
    582
    Thanks
    3

    Solve in R

    Solve in R : $\displaystyle \left( {x^x } \right)^2 = 8$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,237
    Thanks
    33
    Interesting question, I said $\displaystyle x^x = \sqrt{8}$ then using trial and error I found $\displaystyle x \approx 1.788454 $
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    $\displaystyle x^{x}= \sqrt{8} = 2^{3/2} $

    $\displaystyle e^{\ln x \ e^{\ln x}} = 2^{3/2} $

    $\displaystyle \ln (e^{\ln x \ e^{\ln x}}) = \ln (2^{3/2})$

    $\displaystyle \ln x e^{\ln x} =\frac{3}{2} \ln 2$

    $\displaystyle \ln x = \frac{\frac{3}{2}\ln 2}{e^{\ln x}} = W\Big(\frac{3}{2} \ln 2\Big)$

    where W is the Lambert W function

    so $\displaystyle x = e^{W\Big(\frac{3}{2} \ln 2\Big)} \approx 1.788 $
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. need to solve summation equation to solve sum(x2)
    Posted in the Statistics Forum
    Replies: 2
    Last Post: Jul 16th 2010, 10:29 PM
  2. how do i solve this IVP: y'=y^2 -4
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: Feb 24th 2010, 11:14 AM
  3. Replies: 1
    Last Post: Jun 9th 2009, 10:37 PM
  4. how do i solve this?
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Aug 2nd 2008, 02:58 PM
  5. how to solve ..
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: Aug 2nd 2008, 08:17 AM

Search Tags


/mathhelpforum @mathhelpforum