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!!
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*} $