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college alg

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solve the following exponential equation.

(e^x-e^-x)/2=6

what is the exact answer?
x=?

what is the answer approx to 3 decimal places?
x=?

  • college alg - ,

    (e^x-e^-x)/2=6
    e^x - e^-x = 12
    multiply each term by e^x

    (e^x)^2 - 1 = 12e^x
    let y = e^x
    y^2 -1 = 12y
    y^2 - 12y - 1 = 0
    (y-4)(y+3) = 0
    y = 4 or y = -3
    e^x = 4 or e^x = -3 , the latter part being impossible

    so e^x = 4
    take ln of both sides
    ln e^x = ln4
    x lne = ln4
    x = ln4 or appr 1.386

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