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pre-cal

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solve the equation algebraically.

7e^x=11-e^-x

  • pre-cal -

    7 e^x = 11 - 1/e^x

    let e^x = t

    7t = 11 - 1/t
    times t
    7t^2 = 11t - 1
    7t^2 - 11t + 1 = 0
    t = (11 ± √93)/14

    then e^x = (11 + √93)/14 = 1.474546...
    x = ln 1.4745.. = .38835..

    or

    e^x = (11 - √93)/14 = .096882..
    x = ln .096882.. = -2.33426...

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