# logarithms!

• Nov 23rd 2012, 04:03 AM
Tutu
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!!
• Nov 23rd 2012, 04:08 AM
Prove It
Re: logarithms!
Are you trying to simplify \displaystyle \displaystyle \begin{align*} \frac{\frac{\log{\left( 12 \sqrt{3} \right)}}{5 \sqrt{10}}}{\log{\left( \frac{6}{5} \right)}} \end{align*}?
• Nov 23rd 2012, 04:13 AM
Tutu
Re: logarithms!
Rreally sorry. Yep thats the one, just that.it is also lg(5sqrt10), not just 5sqrt10
• Nov 23rd 2012, 04:16 AM
Prove It
Re: logarithms!
So it's \displaystyle \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*}?
• Nov 23rd 2012, 04:19 AM
Tutu
Re: logarithms!
Yes!
• Nov 23rd 2012, 09:46 PM
Prove It
Re: logarithms!
To the OP, all you can do is

\displaystyle \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*}