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Math Help - simple logs

  1. #1
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    simple logs

    hi guys how do expand this log expression?

    log(3��² √��/³√5��²)

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  2. #2
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    Quote Originally Posted by Cockchestner007 View Post
    hi guys how do expand this log expression?

    log(3��² √��/³√5��²)

    Doesn't render properly on my system (Vista Home Basic, Firefox).

    Image: (click for full size)

    simple logs-simplelogs.png
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  3. #3
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    hey man sorry about it, its



    log(3x²√y/³5z²)
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  4. #4
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    Quote Originally Posted by Cockchestner007 View Post
    hey man sorry about it, its



    log(3x²√y/³5z²)
    I can see all the characters now, but I'm still not sure what it's supposed to be.

    Some guesses

    \log\left(\frac{3x^2\sqrt{y}}{\sqrt[3]{5}z^2}\right)

    \log\left(\frac{3x\sqrt{y}}{\sqrt[3]{5z^2}}\right)
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  5. #5
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    its the first guess!~!!
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  6. #6
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    Quote Originally Posted by Cockchestner007 View Post
    its the first guess!~!!
    Applying the rules of logarithms

    \log\left(\frac{3x^2\sqrt{y}}{\sqrt[3]{5}z^2}\right)

    =\log(3x^2\sqrt{y})-\log(\sqrt[3]{5}z^2)

    =\log(3)+\log(x^2)+\log(y^{\frac{1}{2}})-\log(5^{\frac{1}{3}})-\log(z^2)

    =\log(3)+2\cdot\log(x)+\frac{1}{2}\cdot\log(y)-\frac{1}{3}\cdot\log(5)-2\cdot\log(z)
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