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college algebra

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Solve the exponential equation. Express your solutions in exact form only. Please show all of your work.

3^x-70*3^-x=9

  • college algebra -

    multiply each term by 3^x
    3^(2x) - 70 = 9(3^x)
    (3^x)^2 - 9(3^x) - 70=0
    let 3^x = y , our equation becomes
    y^2 - 9y - 70 = 0
    (y-14)(y+5) = 0
    y = 14 or y = -5
    then
    3^x = 14
    log (3^x) = log14
    xlog3 = log14
    x = log14/log3 or appr. 2.402

    or e^x = -5, which has no solution.

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