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Homework Help: Logarithms Calculus help!

  1. Sep 18, 2005 #1
    2^(2x)-2^(x)-6=0
    solve for X..

    im realy lost in this class i just came for one day and the teacher said just try the question using logarithms :S and i dont wahts going on...

    this is what i did

    4x-2x-6=0
    2x-6=0
    x=3...

    but the answer is log2(3)
     
  2. jcsd
  3. Sep 18, 2005 #2
    quadratic equation and logarithms:
    Let 2^x = y.
    Form a quadratic equation.
    Solve the equation.
    Substitute your answer back into 2^x = y.
    Use logarithms to solve for x.
     
  4. Sep 19, 2005 #3

    HallsofIvy

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    Science Advisor

    You "lost" the exponentials! 22x is equal to 4x but 4x is not 4x and 2x is not 2x!

    As Leong suggested, since 22x is also (2x)2, let y= 2x so that your equation becomes the quadratic equation y2-y- 6= (y-3)(y+2)= 0 which has solutions y= 3, y= -2.
    Now you know that y= 2x= 3 and can solve for x using logarithms.
    Of course 2x= -2 is impossible- a positive number to any power is never negative.
     
    Last edited by a moderator: Sep 19, 2005
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