Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to solve 1^x

  1. Sep 22, 2004 #1
    How can I solve this equation ?
    Thanks
     
    Last edited: Sep 22, 2004
  2. jcsd
  3. Sep 22, 2004 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    it is one for all rational x, and hence, if we've any intent on it being continuous it is 1 for all real x, a non-rigorous explanation admittedly but it agrees with the proper exp{xlog1} definition.
     
  4. Sep 22, 2004 #3

    Zurtex

    User Avatar
    Science Advisor
    Homework Helper

    For people who have not spotted there was an edit in the title that has not shown up on the main board. The question s/he is now asking is how to solve:

    [tex](1 + x)^x = x[/tex]
     
  5. Sep 22, 2004 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Did Tombow2885 edit to change to question or was mattgrime just responding to the title?

    The question I see is to solve (1+x)x= x.

    The left hand side is not defined for x< -1. If -1< x< 0, the left hand side is positive and so cannot equal x. The left hand side is not defined for x= 0.
    If 0< x< 1, the right hand side is larger than 1 and so cannot equal x. If x= 1, the equation becomes 2= 1 which is clearly not true.

    If x> 1 (1+x)x> 1+x and so cannot be equal to x.

    You can't solve the equation, it has no solution.
     
  6. Sep 22, 2004 #5
    Oh, I am sorry matt, because the titles still the same even when I edited, I also didn't see your post, okey :wink:, thanks for your answer. :)
     
  7. Sep 22, 2004 #6

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    I responded to the original question which asked what 1^x was for x a positive real number.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: How to solve 1^x
  1. Solve (-1)^x=1 (Replies: 13)

Loading...