Taylor series expansion of base 2 logarithms

Sorry for the noob question, but I've been hitting my head against the wall on this for a while.

I am looking for a Taylor series expansion of a logarithm other than the natural logarithm $ln(x)$. It seems that every piece of literature I've been going through treats solely the natural logarithm and not logarithms in other bases.

In particular, I would like to know the Taylor series corresponding to the binary logarithm $log_2(x)$. For instance, how would I go about calculating $log_2(3)$ using the Taylor series?

Thanks!