Results 1 to 5 of 5
Like Tree2Thanks
  • 1 Post By Reckoner
  • 1 Post By Prove It

Thread: Solve x^y=0.5 for y.

  1. June 18th 2012, 06:43 PM #1
    jasonc2
    jasonc2 is offline
    Newbie
    Joined
    Jun 2012
    From
    United States
    Posts
    5

    Question [solved] Solve x^y=0.5 for y.

    Part of a project I'm working on involves calculating a gamma correction value for a color. My question is: Given x, how do I solve x^y=0.5 for y? I know that 0 < x < 1 and y > 0.

    Right now I'm doing a binary search to solve for y, but I'd rather have a direct, exact solution and I can't figure it out.

    Thanks!
    J
    Last edited by jasonc2; June 18th 2012 at 09:29 PM.
    Follow Math Help Forum on Facebook and Google+
  2. June 18th 2012, 06:50 PM #2
    Reckoner
    Reckoner is offline
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    75
    Awards
    1
    MHF Donor

    Re: Solve x^y=0.5 for y.

    Quote Originally Posted by jasonc2 View Post
    Part of a project I'm working on involves calculating a gamma correction value for a color. My question is: Given x, how do I solve x^y=0.5 for y? I know that 0 < x < 1 and y > 0.

    Right now I'm doing a binary search to solve for y, but I'd rather have a direct, exact solution and I can't figure it out.
    x^y = \frac12

    \Rightarrow\ln x^y = \ln\frac12

    \Rightarrow y\ln x = -\ln2

    \Rightarrow y = -\frac{\ln2}{\ln x}
    Thanks from jasonc2
    Follow Math Help Forum on Facebook and Google+
  3. June 18th 2012, 09:28 PM #3
    jasonc2
    jasonc2 is offline
    Newbie
    Joined
    Jun 2012
    From
    United States
    Posts
    5

    Re: Solve x^y=0.5 for y.

    Awesome, thank you so much! =)
    Follow Math Help Forum on Facebook and Google+
  4. June 18th 2012, 09:39 PM #4
    Prove It
    Prove It is offline
    MHF Contributor Prove It's Avatar
    Joined
    Aug 2008
    Posts
    10,259
    Thanks
    697

    Re: Solve x^y=0.5 for y.

    Quote Originally Posted by Reckoner View Post
    x^y = \frac12

    \Rightarrow\ln x^y = \ln\frac12

    \Rightarrow y\ln x = -\ln2

    \Rightarrow y = -\frac{\ln2}{\ln x}
    Or just \displaystyle \begin{align*} y = \log_{x}{\frac{1}{2}} = -\log_x{2} \end{align*}.
    Thanks from jasonc2
    Follow Math Help Forum on Facebook and Google+
  5. June 19th 2012, 01:30 AM #5
    jasonc2
    jasonc2 is offline
    Newbie
    Joined
    Jun 2012
    From
    United States
    Posts
    5

    Re: Solve x^y=0.5 for y.

    Thanks. I don't have logx available to use, only ln and log10.
    Last edited by jasonc2; June 19th 2012 at 01:33 AM.
    Follow Math Help Forum on Facebook and Google+
« equation | students study all four languages »

Similar Math Help Forum Discussions

  1. How to Solve x/3 - 3 = x/5 - 5 ?
    Posted in the Algebra Forum
    Replies: 4
    Last Post: May 2nd 2011, 01:23 PM
  2. need to solve summation equation to solve sum(x2)
    Posted in the Statistics Forum
    Replies: 2
    Last Post: July 16th 2010, 10:29 PM
  3. solve for x
    Posted in the Trigonometry Forum
    Replies: 8
    Last Post: August 10th 2009, 07:13 AM
  4. Solve for y
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: August 3rd 2009, 11:27 AM
  5. How To Solve Integral of e? And solve velocity?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 9th 2009, 10:37 PM

Search Tags


/mathhelpforum @mathhelpforum