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Math Help - Thinking/InquiryProblem Solving: Logarithms

  1. #1
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    Thinking/InquiryProblem Solving: Logarithms

    I am having some difficulty with this question. All I really know how to do is rewrite it.

    If \log{a}{b} = \frac{1}{x} and  \log{b}{\sqrt{a}} = 3x^2 , show that  x = \frac{1}{6}

    *note: I don't know how to do those logs better... it is saying "log base a" and the other one is "log base b"*

    I have tried everything I could think of. I subbed in 1/6 for x, made them into exponent form, but I don't know how to answer this question. Or even what it's asking.

    Help?
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  2. #2
    MHF Contributor red_dog's Avatar
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    \log_b\sqrt{a}=\frac{1}{2}\log_ba=3x^2\Rightarrow\  log_ba=6x^2.

    But \log_ab\cdot\log_ba=1.

    Then \frac{1}{x}\cdot 6x^2=1\Rightarrow 6x=1\Rightarrow x=\frac{1}{6}
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