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Posted by on Thursday, January 13, 2011 at 7:06pm.

logof3(x-1)+ logof3(3x-1)=2

  • Algebra 2 Trig Honors - , Saturday, January 15, 2011 at 3:21pm

    Log((3X - 3)(9X - 3)) = 2.

    (3X - 3)(9X - 3) = 10^2,
    27X^2 - 9X - 27X + 9 = 100,
    27X^2 - 36X + 9 = 100,
    27X^2 - 36X + 9 - 100 = 0,
    27X^2 - 36X - 91 = 0,

    Using the Quadratic Formula:
    X = (36 +- sqrt(1296 - (- 9828))) / 54,
    X = (36 +- sqrt(1296 + 9828)) / 54,
    X = (36 +- sqrt(11124)) / 54,
    X = (36 +- 105.5) / 54,

    X = 2.62, and X = -1.29.

    Check:
    Log((3*2.62 - 3)(9*2.62 - 3) =
    Log(7.86 - 3)(23.58 - 3) =
    Log(4.86 * 20.58) =

    Log(100.019) = 2.000.

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