Maclaurin expansion problem I am having problem with a question regarding Maclaurin expansion. 
a) Find the term up to $x^4$ in the Maclaurin expansion of $f(x)=\ln(\cos(x))$.
This part I was able to anwser part a. The Maclaurin expansion until $x^4$ is: $f(x)=-x^2/2-x^4/12$
b) Use this series to find an approximation in terms of $\pi$ for $\ln(2)$. 
I was not able to answer part b. If someone know how to make it I would appreciate it.
Thanks

Hint: Use the fact that $\ln(a^b)=b\cdot\ln(a)$. Therefore, $\ln(2)=-\ln\bigl(\frac{1}{2}\bigr)$. Then, when does $\cos(x)=\frac{1}{2}$?
