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math

posted by on .

solve the following exponential equation:show your work.
e^x-e^-x/2=7
1. write exact answer.
2.write answer approximated to 3 decimal places.

whaaaat? smh I don't get it at all.

  • math - ,

    If you mean
    (e^x - e^-x)/2 = 7
    e^x - e^-x = 14
    e^2x - 1 = 14e^x
    e^2x - 14e^x - 1 = 0
    Now you just have a quadratic in e^x, so
    e^x = (14±√200)/2
    = 7±5√2
    e^x is never negative, so
    e^x = 7+5√2
    x = ln(7+5√2) = 2.644

    Or, more directly, recognize that what you have is

    sinh(x) = 7
    x = 2.644

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