Results 1 to 3 of 3

Math Help - Solving logarithmic equation

  1. #1
    Member
    Joined
    Feb 2008
    From
    Westwood, Los Angeles, CA
    Posts
    176
    Thanks
    1

    Solving logarithmic equation

    I think I solved this correctly, but could use an extra set of eyes.

    ln(3 \sqrt{x}) = \sqrt{ln x}.

    Working on the left:

    ln (3 \sqrt{x}) = ln 3 + ln \sqrt{x} = ln 3 + \frac{1}{2}ln{x}

    so now I have:

    ln 3 + \frac{1}{2}ln{x} = \sqrt{ln x}

    I made the substitution u = \sqrt{ln x}, so u^2 = ln x. Performing this substitution gives:

    ln 3 + \frac{1}{2}u^2 = u.

    Moving everything to one side:

    \frac{1}{2}u^2 - u + ln 3 = 0.

    A quadratic in u, so using the quadratic formula with a = .5, b = -1, c = ln 3, my discriminant is:

    1 - 2 ln 3.

    My discriminant is negative, so I have no real solution for u, and thus no real solution for the whole thing.

    Look okay? The way the problem was phrased in the text really suggests there's an answer, but...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    Looks good to me
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by Mathnasium View Post
    I think I solved this correctly, but could use an extra set of eyes.
    ...
    My discriminant is negative, so I have no real solution for u, and thus no real solution for the whole thing.

    Look okay? The way the problem was phrased in the text really suggests there's an answer, but...
    All your considerations and calculations are OK.

    As an additional information I've attached the graphs of

    f(x) = \ln(3\sqrt{x}) ...... and ...... g(x) = \sqrt{\ln(x)}

    The graphs don't intersect that means there doesn't exist a real x so that both terms are equal.
    Attached Thumbnails Attached Thumbnails Solving logarithmic equation-zweilogfkt.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Having Trouble Solving Logarithmic Equation
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 17th 2011, 03:40 PM
  2. Solving a weird logarithmic equation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 6th 2011, 02:07 PM
  3. Solving a logarithmic equation
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: May 3rd 2010, 08:35 AM
  4. Need help in solving logarithmic equation
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: April 2nd 2009, 05:07 PM
  5. Solving logarithmic equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 18th 2007, 02:43 PM

Search Tags


/mathhelpforum @mathhelpforum