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Math Help - Exponential Equation With Number e

  1. #1
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    Exponential Equation With Number e

    Solve the exponential equation below. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.

    [e^(x) - e^(-x)]/2 = -2

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  2. #2
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    \frac{e^x - e^{-x}}{2} = -2

    multiply both sides by 2 ...

    e^x - e^{-x} = -4

    multiply every term by e^x ...

    (e^x)^2 - 1 = -4e^x

    (e^x)^2 + 4e^x - 1 = 0

    let u = e^x

    u^2 + 4u - 1 = 0

    use the quadratic formula to solve for u, then use the natural log (ln) to solve for x.
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  3. #3
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    Very good...

    I can take it from here.

    Good job!
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