Results 1 to 4 of 4

Thread: equation a^x=x

  1. #1
    Newbie
    Joined
    Dec 2018
    From
    Romania
    Posts
    7

    equation a^x=x

    If the equation a^x=x with a>1 has one solution then:
    A)a=1/e
    B)a=e
    C)a=e^(1/e)
    D)a=e^e
    E)1/(e^e)
    The right answer is C.I tried to derivate then to resolve f'(x) but didn't work
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    20,078
    Thanks
    3211

    Re: equation a^x=x

    That is simply not true! Graphing $y= (1/e)^x- x$ (A), $y= (e^{1/e})^x- x$ (C), and $y= (1/e^e)^x- x$ (E) we have graphs that cross the x-axis exactly once.
    Last edited by topsquark; Dec 29th 2018 at 01:42 PM. Reason: Tweaked LaTeX
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Dec 2013
    From
    Colombia
    Posts
    1,964
    Thanks
    701

    Re: equation a^x=x

    $a=\frac1e < 1$ so it can't be a solution because the question states that $a > 1$. Similarly for $\frac1{e^e}$.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Dec 2018
    From
    Romania
    Posts
    7

    Re: equation a^x=x

    I did it with some help from another user
    f(x)=a^x-x=0
    f'(x)=a^xlna-1=0
    a^xlna = 1 => a^x = 1/lna (from f'(x)=0)
    But a^x=x (from initial equation) si x=1/lna=log_a(e)=>a^x=e => e=1/lna=> a=e^(1/e)
    Last edited by Vali; Dec 29th 2018 at 12:57 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Single second order partial differential equation (heat equation)
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: Mar 8th 2015, 01:59 PM
  2. Replies: 1
    Last Post: Dec 2nd 2013, 07:20 AM
  3. Replies: 2
    Last Post: Feb 25th 2013, 10:32 PM
  4. Replies: 1
    Last Post: Apr 11th 2011, 02:17 AM
  5. Partial differential equation-wave equation - dimensional analysis
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: Aug 28th 2009, 12:39 PM

/mathhelpforum @mathhelpforum