$\displaystyle 2log_{4}9 - log_{2}3$ is what i need to simplify
You need to use the change of base rule
$\displaystyle \log_b{x} = \frac{\log_k{x}}{\log_k{b}}$.
I always use natural logs, but you can choose whatever base you like.
$\displaystyle 2\log_4{9} - \log_2{3} = \frac{2\ln{9}}{\ln{4}} - \frac{\ln{3}}{\ln{2}}$
$\displaystyle = \frac{4\ln{3}}{2\ln{2}} - \frac{\ln{3}}{\ln{2}}$
$\displaystyle = \frac{2\ln{3}}{\ln{2}} - \frac{\ln{3}}{\ln{2}}$
$\displaystyle = \frac{\ln{3}}{\ln{2}}$
$\displaystyle = \log_2{3}$.