Estimate ln(3) using Taylor Expansion up to 3rd order (without the use of a calculator).
$$f(x)=ln(x)$$ $$f'(x)=1/x$$ $$f''(x)=-1/x^2$$ $$f'''(x)=2/x^3$$
If I let a=2, I can solve for the first to third order, but I will then have to estimate f(2)=ln(2). Using the same method as above to estimate ln(2), i.e. a=1, I will have a rather inaccurate estimate of ln(2).
Is there any other ways to estimate ln(3) more accurately?