1. ## laws of logs?

I have almost completed the question. I am using the mark scheme to check my answers and i have managed to correctly get to this line

-ln2 + ln1 + 4ln3 - 4ln2 - 3ln4 + 3ln3

Now the mark scheme jumps from this straight to this

-11n2 + 7ln3

Could anybody show me how this is done?

I know ln1 = 0 and the coefficients of ln can become the power but i still dont see how it works :s

2. Just notice that $\displaystyle 3\ln (4) = 3\ln (2^2 ) = 6\ln (2)$.

3. Sneaky! thanks!