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Math Help - Exponential

  1. #1
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    Exponential

    Gosh, i know the basic of exponentials, but when it contains some complex algebra stuff in there, i go blank.

    I know to subtract the 10, but thats it...

    e^2x-7e^x + 10 = 0 (its e to the 2x power)


    Thanks a bunch!
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  2. #2
    Junior Member woof's Avatar
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    Solve for x: e^{2x}-7e^x + 10 = 0 (you need to surround your exponent with braces if it has more than one item in it).


    Let u=e^x, and then you have the quadratic u^{2}-7u+ 10 = (u-2)(u-5)=0, and therefore

    u=5 or u=2

    e^x=5 or e^x=2

    Then x=ln 5 or x=ln 2
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  3. #3
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    Is there another way without using variable = e^x?
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  4. #4
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    Do you mean "is there a harder way"? Of course, you don't have to replace e^x, that's just the simplest thing to do. You could recognise that e^{2x}- 7e^x+ 10= (e^x- 2)(e^x- 5)= 0 and then arguing that either e^x- 2= 0 or e^x- 5= 0.

    And how do I recognise that factoring? Well, I recognize e^{2x}- 7e^x+ 10 as a "quadratic in e^x" which is essentially replacing e^x, at least in my head, by a single variable.
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