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Homework Help: Exponential Equations

  1. Jul 26, 2010 #1
    I just want to make sure that I have this in the correct order. The book I have is very unclear.

    e^x + e^-x = 6
    e^x + 1/e^x = 6
    e^2x + 1 = 6e^x
    e^2x/e^x + 1 = 6
    x = ln 6

    Thanks.
     
  2. jcsd
  3. Jul 26, 2010 #2

    Mute

    User Avatar
    Homework Helper

    You've made a mistake. The fourth line doesn't follow from the third. It looks like you tried to divide by e^x (which is actually just undoing what you did in going from line 2 to 3), but you forgot to divide the 1 by e^x.

    What you should do is rearrange your third line so that it looks like

    e^(2x) - 6e^x + 1 = 0.

    Does this look like a familar sort of equation? (If not, let y = e^x. Then does it look familar?)
     
  4. Jul 26, 2010 #3
    Thanks a lot. I thought something looked off. The thing that worried me is that the answer that I got is quite approximate, and I wanted to make sure that I was doing the process correctly, which I wasn't.

    Then after this I would simply do the U form of the quadratic, correct?
     
  5. Jul 26, 2010 #4

    Mark44

    Staff: Mentor

    Yes, the equation is quadratic in form, so a substitution will make it a quadratic, which you can solve using the quadratic formula.
     
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