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Math Help - e^x equation

  1. #1
    Senior Member Twig's Avatar
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    e^x equation

    Hi!

    (e^x)^2 - 5e^x + 6 = 0

    how should I start?

    I tried setting e^x = y

    then -> y^2 - 5y + 6 = 0

    solving this I get the roots 3 and 2

    Am I doing this wrong?

    UH ok =) I just found out this -> I get answers y=3 and y=2 .. I take e^x = 3 and e^x = 2
    then I take ln 3 and ln 2 and I get the correct answer.

    Just as a note.
    What are the common situations for using the method of calling e^x = y ?

    thanks!
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  2. #2
    Moo
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    A Cute Angle Moo's Avatar
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    Hello,

    It's correct (if i haven't gone too fast).

    Now, solve for x.

    You know that y=3=e^x and y=2=e^x are solutions
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Twig View Post
    Just as a note.
    What are the common situations for using the method of calling e^x = y ?
    good job.

    the common situations you will be able to identify using experience, but pretty much anywhere where you see the problem can be simplified into a form you are more familiar with (like in this case, it simplified to a quadratic equation) this technique can be used. it is mostly for visualization purposes though, you could have just as well solved the problem without it. (e^x)^2 - 5e^x + 6 = (e^x - 3)(e^x - 2) \implies e^x = 3 \mbox{ or } e^x = 2 \cdots
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