Changing domain in numerical method for ln(x)

Question

Say for instance I have found a method for numerically calculating $ln(x)$ for values of $x$ between $\frac 12$ and $\frac 32$. How would I extend the method I already have so that the method works for all $x>0$? I imagine I'd have to use the logarithmic laws to manipulate $ln(x)$ somehow, but I honestly don't know where to go from here.