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Calculus problem which requires me to isolate X

  1. Sep 9, 2008 #1
    I'm solving a calculus problem which requires me to equate both equations, but I can't isolate X:

    √x = e^-3x

    What I've got so far is:

    ln√x = ln e^-3x

    ln√x = -3x

    1/2 ln x = -3x

    ln x = -6x .... but from here I can't continue, please help:frown:
  2. jcsd
  3. Sep 9, 2008 #2
    you mean you want to solve for x right?? well, i dont think that can be done in terms of standard functions.
  4. Sep 9, 2008 #3
    Yeah, like said, i can only show that a sol, to this eq exists, but i don't believe there is a solution algebraically. YOu can only solve it numerically.
  5. Sep 10, 2008 #4

    Gib Z

    User Avatar
    Homework Helper

    I have quite a remarkable exact solution -

    The GibZ Constant - G​

    where G is defined to be the unique solution to the equation [itex]log_e x + 6x = 0[/itex] lol.
  6. Sep 10, 2008 #5
    well if ya got to here , heh , just a thought

    ln x = -6x

    take e to both sides
    and get x=e^-6x

  7. Sep 10, 2008 #6

    ...and...end up with exactly what you started with...lol....
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