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Math Help - determine the value of a

  1. #1
    rcs
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    determine the value of a

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  2. #2
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    ab = a^b and \frac{a}{b} = a^{3b}.

    Rearranging the second equation gives b = \frac{a}{a^{3b}} = a^{1 - 3b}.

    Substituting into the first gives

    a(a^{1 - 3b}) = a^b

    a^{2 - 3b} = a^b

    2 - 3b = b

    2 = 4b

    b = \frac{1}{2}.


    Back substituting gives

    b = a^{1 - 3b}

    \frac{1}{2} = a^{1 - \frac{3}{2}}

    \frac{1}{2} = a^{-\frac{1}{2}}

    2 = a^{\frac{1}{2}}

    a = 4.
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