1. Simplifying logarithm problem

$2log_{4}9 - log_{2}3$ is what i need to simplify

2. Originally Posted by zooply
$2log_{4}9 - log_{2}3$ is what i need to simplify

Note that:

$log_{2}3 = \frac{log_{10} 3}{log_{10} 2} = 2 \frac{log_{10} 3}{2 log_{10} 2} = 2 \frac{log_{10} 3}{log_{10} 4} =2 log_{4} 3 = log_{4} 9$

Does this help?

3. Originally Posted by zooply
$2log_{4}9 - log_{2}3$ is what i need to simplify
You need to use the change of base rule

$\log_b{x} = \frac{\log_k{x}}{\log_k{b}}$.

I always use natural logs, but you can choose whatever base you like.

$2\log_4{9} - \log_2{3} = \frac{2\ln{9}}{\ln{4}} - \frac{\ln{3}}{\ln{2}}$

$= \frac{4\ln{3}}{2\ln{2}} - \frac{\ln{3}}{\ln{2}}$

$= \frac{2\ln{3}}{\ln{2}} - \frac{\ln{3}}{\ln{2}}$

$= \frac{\ln{3}}{\ln{2}}$

$= \log_2{3}$.