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Math Help - logarithms!

  1. #1
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    logarithms!

    Help! What.do.I do with (lg(12sqrt3)/(5sqrt10))/lg(6/5)?? Im really sorry it's hard to read and decipher the logarithms but I'd really appreciate and need this! Thanks!!
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    Re: logarithms!

    Are you trying to simplify \displaystyle \begin{align*} \frac{\frac{\log{\left( 12 \sqrt{3} \right)}}{5 \sqrt{10}}}{\log{\left( \frac{6}{5} \right)}} \end{align*}?
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    Re: logarithms!

    Rreally sorry. Yep thats the one, just that.it is also lg(5sqrt10), not just 5sqrt10
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    Re: logarithms!

    So it's \displaystyle \begin{align*} \frac{\frac{\log{\left( 12\sqrt{3} \right)}}{\log{\left( 5\sqrt{10} \right)}}}{\log{\left( \frac{6}{5}\right)}} \end{align*}?
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  5. #5
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    Re: logarithms!

    Yes!
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  6. #6
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    Re: logarithms!

    To the OP, all you can do is

    \displaystyle \begin{align*} \frac{\frac{\log{\left( 12\sqrt{3} \right)}}{\log{\left( 5\sqrt{10} \right)}}}{\log{\left( \frac{6}{5} \right)}} &= \frac{\log{\left( 12\sqrt{3} \right)}}{\log{\left( 5\sqrt{10} \right)} \log{\left( \frac{6}{5} \right)}} \\ &= \frac{ \log{ \left( 432^{\frac{1}{2}}  \right) } }{ \log{ \left( 250^{\frac{1}{2}} \right) } \left[ \log{(6)} - \log{(5)} \right] } \\ &= \frac{\frac{1}{2}\log{(432)}}{\frac{1}{2}\log{(250  )} \left[ \log{(6)} - \log{(5)} \right] } \\ &= \frac{\log{(432)}}{\log{(250)}\left[ \log{(6)} - \log{(5)} \right]}\end{align*}
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