How can I find the value of $\ln( |x|)$ without using the calculator? I want to know if there is a way to find for example $\ln(2)$, without using the calculator ?
Thanks 

$$\log 2 = 1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\ldots$$
In the general case
$$\log \frac{1+x}{1-x} = 2(x+\frac{x^3}{3}+\frac{x^5}{5}+\frac{x^7}{7}+\ldots)$$
