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Math Help - Logarithm equation

  1. #1
    Junior Member
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    Nov 2006
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    Logarithm equation

    Please solve for this

    e^(x) - e^(-x)=2
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, camherokid!

    Solve for x: .e^x - e^{-x} .= .2

    Multiply by e
    ^x: .e^{2x} - 1 .= .2e^x

    And we have: . (e
    ^x) - 2e^x - 1 .= .0 . . . a quadratic equation

    . . . . . . . . . . . . . . . . . . . . . . . . __________
    . . . . . . . . . . . . . . . . . . . . 2 √2 - 4(1)(-1)
    Quaratic Formula: . e
    ^x .= . ----------------------- . = . 1 √2
    . . . . . . . . . . . . . . . . . . . . . . . . 2(1)


    Since e
    ^x is positive: . e^x .= .1 + √2

    . . Therefore: . x .= .ln(1 + √2)

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