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Math Help - an a level exponential

  1. #1
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    an a level exponential

    Hello, i have just finished one of my A level papers, i think i aced it except for the first question, and any fluffy mistakes i made.

    e^x +3e^-x = 4

    solve it!

    after the customery after test discussion there seemed to be a differant answer for each student, and in one special case 4.

    Can anybody please solve this question for me, as its bugging me pretty badly.

    Thank you
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  2. #2
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    Quote Originally Posted by pablohacker View Post
    Hello, i have just finished one of my A level papers, i think i aced it except for the first question, and any fluffy mistakes i made.

    e^x +3e^-x = 4

    solve it!

    after the customery after test discussion there seemed to be a differant answer for each student, and in one special case 4.

    Can anybody please solve this question for me, as its bugging me pretty badly.

    Thank you
    e^x +3e^{-x} = 4<-- Multiply both sides by e^x

    e^{2x} + 3 = 4e^x

    e^{2x} - 4e^x + 3 = 0

    Let y = e^x

    Then
    y^2 - 4y + 3 = 0

    (y - 1)(y - 3) = 0

    Thus
    y = 1 ==> e^x = 1 or x = 0
    or
    y = 3 ==> e^x = 3 or x = ln(3)

    -Dan
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