precalculus

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solve exponential equation. express in exact form.
e^x-42e^-x= -19

  • precalculus -

    multiply each term by e^x

    (e^x)^2 - 42 + 19e^x = 0
    let y = e^x
    y^2 + 19y - 42 = 0
    (y+21)(y-2) = 0
    y = -21 or y = 2

    so e^x = 2
    x = ln 2

    or

    e^x = -21, which has no solution

    x = ln2

  • precalculus -

    thanks again

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