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Math Help - Simple Logarithmic Equation Clarification.

  1. #1
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    Simple Logarithmic Equation Clarification.

    Hi all,

    Just another logarithmic question here. I need to solve logx (3) = 1/2 for x and I am not sure why the answer is 9. I think it has something to do with square roots, but I am not confident of the logical order in which that would appear.

    From the above I gather that x is the base, 1/2 is the power, and 3 is the numeral found.

    So:

    x (to the power of 1/2) = 3.

    I am just not sure why one would have to square root 9.

    Sorry if it is a silly question. Any help much appreciated!

    Thanks,

    Nathaniel
    Last edited by mr fantastic; September 21st 2010 at 01:16 AM. Reason: deleted words irrelevant to the purpose of a post title.
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  2. #2
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    x^{\frac{1}{2}}=\sqrt{x}. Generally, x^{\frac{1}{n}}=\sqrt[n]{x}.
    So you have \sqrt{x}=3. Square the equation and there you have it: 9.
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  3. #3
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    Quote Originally Posted by BinaryBoy View Post
    Hi all,

    Just another logarithmic question here. I need to solve logx (3) = 1/2 for x and I am not sure why the answer is 9. I think it has something to do with square roots, but I am not confident of the logical order in which that would appear.

    From the above I gather that x is the base, 1/2 is the power, and 3 is the numeral found.

    So:

    x (to the power of 1/2) = 3.

    I am just not sure why one would have to square root 9.

    Sorry if it is a silly question. Any help much appreciated!

    Thanks,

    Nathaniel
    By definition \displaystyle \log_A B = C \Leftrightarrow A^C = B.

    Therefore \displaystyle \log_x 3 = \frac{1}{2} \Leftrightarrow x^{1/2} = 3.

    Square both sides to get x.
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  4. #4
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    That was a huge help MathoMan and Mr Fantastic. I guess I just have to really know and understand those basic logarithmic rules.

    Thanks!!!
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