Results 1 to 4 of 4

Math Help - Solving Y in terms of X

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    7

    Question Solving Y in terms of X

    i'm having some trouble remembering how to solve this in terms of x.
    y=(e^x-e^-^x)/2

    This is what i was thinking, but, i'm not sure if it is right or not.
    x=(e^y-e^-^x)/2
    2x=(e^y-e^y)
    log(2x)=2y*log(e)
    log(2x)/(2*log(e))=y

    y=log(2x)/(2*log(e))
    I feel like this is not the right answer though :/
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    769
    Quote Originally Posted by fenderic View Post
    i'm having some trouble remembering how to solve this in terms of x.
    y=(e^x-e^-^x)/2

    This is what i was thinking, but, i'm not sure if it is right or not.
    x=(e^y-e^-^x)/2
    2x=(e^y-e^y)
    log(2x)=2y*log(e)
    log(2x)/(2*log(e))=y

    y=log(2x)/(2*log(e))
    I feel like this is not the right answer though :/
    I think the answer you're looking for is y = sinh(x) (or is it cosh(x), it's been awhile since I studied calculus).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,719
    Thanks
    635
    Hello, fenderic!

    i'm having some trouble remembering how to solve this in terms of x.

    . . y\:=\:\dfrac{e^x-e^{-x}}{2}

    It is already "solved in terms of \,x."
    I must assume you mean: "Solve for \,x in terms of \,y."


    We have: . \dfrac{e^x - e^{-x}}{2} \;=\;y \quad\Rightarrow\quad e^x - e^{-x} \;=\;2y

    Multiply by e^x\!:\;\;e^{2x} - 1 \;=\;2ye^x \quad\Rightarrow\quad (e^x)^2 - 2y(e^x) - 1 \;=\;0

    Quadratic Formula: . e^x \:=\:\dfrac{2y \pm\sqrt{4y^2+4}}{2} \quad\Rightarrow\quad e^x \;=\;y \pm \sqrt{y^2+1}

    Since e^x is always positive, we take the positive root: . e^x \;=\;y + \sqrt{y^2+1}

    ,. . Therefore: . x \;=\;\ln\left(y + \sqrt{y^2+1}\right)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2010
    Posts
    7
    thank you Soroban!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. solving y=tanh(y-x) in terms of x
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 9th 2010, 02:34 PM
  2. Replies: 2
    Last Post: November 9th 2009, 03:22 PM
  3. Solving for One Variable in Terms of Others...
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: June 28th 2009, 12:12 PM
  4. solving for y in terms of x
    Posted in the Algebra Forum
    Replies: 7
    Last Post: December 15th 2008, 07:47 PM
  5. Replies: 4
    Last Post: June 6th 2007, 03:05 PM

Search Tags


/mathhelpforum @mathhelpforum