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Thread: log problem

  1. #1
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    log problem

    solve the following equation

    $\displaystyle \log_{\sqrt x}16-\log_{\sqrt x}2=3$
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  2. #2
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    Quote Originally Posted by mastermin346 View Post
    solve the following equation

    $\displaystyle \log_{\sqrt x}16-\log_{\sqrt x}2=3$
    use this property of logarithms on the left side of the equation ...

    $\displaystyle \log_a{m} - \log_a{n} = \log_a\left(\frac{m}{n}\right)
    $

    ... then convert the resulting log equation to an exponential equation and solve for x.
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  3. #3
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    $\displaystyle \log_{\sqrt{x}}8 = 3$

    $\displaystyle \sqrt{x} ^ {log_{\sqrt{x}}8} = \sqrt{x} ^ 3$

    $\displaystyle 8 = x ^ \frac{3}{2}$

    $\displaystyle x = 8 ^ \frac{3}{2}$

    $\displaystyle x = 4$
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  4. #4
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    Quote Originally Posted by Subcydian View Post
    $\displaystyle \log_{\sqrt{x}}8 = 3$

    $\displaystyle \sqrt{x} ^ {log_{\sqrt{x}}8} = \sqrt{x} ^ 3$

    $\displaystyle 8 = x ^ \frac{3}{2}$

    $\displaystyle x = 8 ^ \frac{3}{2}$

    $\displaystyle \textcolor{red}{x = 8^{\frac{2}{3}}}$

    $\displaystyle x = 4$
    ...
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