Question 1115168
You didn't mention how but I'm going to use a Taylor series expansion.
{{{ln(x)=(x-1)-(x-1)^2/2+(x-1)^3/3-(x-1)^4/4+(x-1)^5/5}}}
{{{ln(2)=(2-1)-(2-1)^2/2+(2-1)^3/3-(2-1)^4/4+(2-1)^5/5}}}
{{{ln(2)=1-1/2+1/3-1/4+1/5-1/6+1/7-1/8+1/9-1/10+1/11-1/12}}}
You can continue to add terms to get closer to the real value,
{{{ln(2)=18107/27720}}}
or 
{{{ln(2)=0.6532}}}
compared to the real value of 
{{{ln(2)=0.6931}}}