logarithms!

**Tutu** · November 23rd 2012, 04:03 AM

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!!

**Prove It** · November 23rd 2012, 04:08 AM

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

**Tutu** · November 23rd 2012, 04:13 AM

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

**Prove It** · November 23rd 2012, 04:16 AM

So it's $\displaystyle \begin{align*} \frac{\frac{\log{\left( 12\sqrt{3} \right)}}{\log{\left( 5\sqrt{10} \right)}}}{\log{\left( \frac{6}{5}\right)}} \end{align*}$ ?

**Tutu** · November 23rd 2012, 04:19 AM

Yes!

**Prove It** · November 23rd 2012, 09:46 PM

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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