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Math Help - Simultaneous Equations Logarithms Problem

  1. #1
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    Simultaneous Equations Logarithms Problem

    the base is inside the ()

    y=2log(3)x

    y+1=log(3)9x

    what i did:

    y=2log(3)x
    y=log(3)9x-1

    2log(3)x = log(3)9x-1
    2log(3)x = 2log(3)3X - log(3)3
    2log(3)x - 2log(3)3x = - log(3)3
    x(2log(3)1 - 2log(3)3) = -log(3)3
    x = -log(3)3 / (2log(3)1 - 2log(3)3)
    x = -1 / (0-2)
    x = 1/2

    however, the answer is x=3

    could you tell me hwere i went wrong please?
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by juliak View Post
    the base is inside the ()

    y=2log(3)x

    y+1=log(3)9x

    what i did:

    y=2log(3)x
    y=log(3)9x-1

    2log(3)x = log(3)9x-1
    2log(3)x = 2log(3)3X - log(3)3
    2log(3)x - 2log(3)3x = - log(3)3
    x(2log(3)1 - 2log(3)3) = -log(3)3
    x = -log(3)3 / (2log(3)1 - 2log(3)3)
    x = -1 / (0-2)
    x = 1/2

    however, the answer is x=3

    could you tell me hwere i went wrong please?
    Hi juliak,

    Here we go....

    2\log _3 (x)=\log_3 (9x)-1

    2\log_3 (x)=\log_3(9)+\log_3(x)-1

    2\log_3(x)=2+\log_3(x)-1

    2\log_3(x)=\log_3(x)+1

    \log_3(x)=1

    x=3^1

    x=3
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