Here's the question:

Calculate the Taylor polynomial T1,n(x) for f(x) = ln x

a. How many decimal digits are guaranteed in approximation of ln 1.5 by T1,10(1.5)?

b. What degree Taylor polynomial will guarantee the above approximation to four decimal digits?

I have read my professor's notes, but it is hard to understand them so if somebody could clarify to me the steps involved in solving this problem it would be much appreciated.