1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Rearranging (1+x)e^-x = 0.5

  1. Jan 6, 2008 #1
    Sorry if this is a very simple question, I am trying to rearrange (1+x)e^-x = 0.5 for x, and just can't seem to get my head around it. Any tips would be greatly appreciated.
  2. jcsd
  3. Jan 6, 2008 #2
    Take log on both sides and go from there.
  4. Jan 6, 2008 #3
    Take the natural log of both sides and then use the properties of log to split the left side.

    [tex]\ln(a/b)=\ln a - \ln b[/tex]

    And remember that [tex]\ln e = 1 = \mbox{cancels each other out}[/tex]
    Last edited: Jan 6, 2008
  5. Jan 6, 2008 #4
    This is where I've got to, thanks for the responses:

    ln((1+x)/e^x) = ln0.5
    ln(1+x)-x =ln0.5
    Last edited: Jan 6, 2008
  6. Jan 6, 2008 #5
    I can't seem to go anywhere from your last step, is the problem written down correctly?
  7. Jan 6, 2008 #6


    User Avatar
    Science Advisor
    Homework Helper

    do you have to solve this analytically?
  8. Jan 6, 2008 #7


    User Avatar
    Science Advisor
    Homework Helper

    It's certainly impossible to solve analytically.
  9. Jan 6, 2008 #8


    User Avatar
    Science Advisor
    Homework Helper

    yes, thats why I asked the OP ;)
  10. Jan 6, 2008 #9


    User Avatar
    Science Advisor

    In general, a problem involving "x" both in an exponent and not can only be solved using the "Lambert W function" which is defined as the inverse function to f(x)= xex- and may require manipulation of the equation to put it in that form.
  11. Jan 16, 2008 #10
    I don't know if i'm doing this right, but here are my thoughts. if you factor out the first side you get xe^x+e^x=0.5 Then if you divide both sides by x you get e^x+e^x=0.5/x add your like terms on the left and you get 2e^x=0.5/x (i think that's right)
    See if you can get it from there
    ((i just realized that this was from over a week ago AFTER i finished lol))
  12. Jan 16, 2008 #11
    That's wrong, read all the posts before yours.
  13. Jan 16, 2008 #12
    sorry, i also didn't read the original question right *sigh*
  14. Jan 16, 2008 #13
    It's ok, no worries.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook