Results 1 to 4 of 4

Thread: Solving for x in equations involving logs

  1. #1
    Newbie
    Joined
    Jun 2010
    Posts
    6

    Solving for x in equations involving logs

    Could somebody point me in the right direction?

    $\displaystyle e^x + e^-^x = 2$
    $\displaystyle e^x (e^x + e^-^x) = 2*e^x$
    $\displaystyle e^2x + e = 2e^x$
    $\displaystyle e^2x - 2e^x + e = 0$

    Something tells me I should be able to solve this as a quadratic, but e is a constant, and I can't figure out how to do this with a constant as the base.
    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
    $\displaystyle e^x+e^{-x}=2$

    Times both sides by $\displaystyle e^x$

    $\displaystyle e^{2x}+1=2 e^x $

    $\displaystyle e^{2x}-2 e^x+1=0 $

    make $\displaystyle e^x = a$ giving

    $\displaystyle a^{2}-2 a+1=0 $

    Solve from here?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2010
    Posts
    6
    Ok, but why is $\displaystyle e^x * e^-^x$ =1? Why isn't it $\displaystyle e$?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,237
    Thanks
    33
    $\displaystyle e^x\times e^{-x}= e^{x-x}= e^0 = 1$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. help solving an equation involving logs
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Oct 6th 2009, 07:45 AM
  2. Solving simultaneously involving logs.
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Jul 19th 2009, 04:51 AM
  3. Replies: 2
    Last Post: Feb 2nd 2009, 04:14 PM
  4. Solving equations involving logs
    Posted in the Algebra Forum
    Replies: 8
    Last Post: Jun 8th 2008, 07:50 PM
  5. solving for x, involving logs
    Posted in the Algebra Forum
    Replies: 6
    Last Post: Jun 8th 2008, 12:13 PM

Search Tags


/mathhelpforum @mathhelpforum