precalculus

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Solve the logarithmic equation. Express your solutions in exact form only.
18e^-x -e^x=7

  • precalculus -

    18/e^x - e^x = 7
    let e^x = a

    18/a - a - 7 = 0
    18 - a^2 - 7a = 0
    a^2 + 7a - 18 = 0
    (a+9)(a-2) = 0
    a = -9 or a = 2
    then
    e^x = -9 ----> no solution
    or
    e^x = 2
    x = ln 2

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