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Please help quick!! Mathematics A

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Solve for x: 9^x-3^x-8=0

  • Please help quick!! Mathematics A - ,

    (3^2)^x-3^x-8=0,
    (3^x)² -3^x -8 = 0,
    3^x =y,
    y² -y - 8=0,
    y= (1±√33)/2.
    Since 3^x>0, the negative root is nonsence,
    => y= (1+√33)/2 =3.37228,
    3^x =3.37228,
    x=log(3)3.37228= =ln3.37228/ln3≈1.21559/1.0986=1.1065

    Test:
    9^1.1065 – 3^1.1065 – 8 =
    =11.372 – 3.372 – 8 = 0

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