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Math Help - e and ln

  1. #1
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    e and ln

    I have half done this question and icant seem to finish it im completely suck.. so any help is appreciated

    Find the exact values of x for which...

    (e^x)/(((e^x)-2)^2) = 1
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  2. #2
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    Quote Originally Posted by pop_91 View Post
    I have half done this question and icant seem to finish it im completely suck.. so any help is appreciated

    Find the exact values of x for which...

    (e^x)/(((e^x)-2)^2) = 1
    It's refreshing to see a unambiguously written equation

    \frac{e^x}{(e^x -2)^2} = 1

    e^x = (e^x-2)^2

    Expand the right hand size as per the binomial theorem/normal quadratic

    e^x = (e^x)^2 - 4e^x + 4

    (e^x)^2 - 5e^x +4 = 0

    This is a quadratic in e^x and so the quadratic equation can be used - however this one factorises

    (e^x-4)(e^x-1) = 0

    Spoiler:
    e^x = 4 \: \rightarrow \: x = 2ln2

    e^x = 1 \: \rightarrow \: x = 0
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