The Taylor series expansion of ln(x) around a point x = a is ln(x) = ln(a) + (x-a)/a - ((x-a)^2)/(2 a^2) + ((x-a)^3)/(3 a^3) - ...

The Taylor series of ln(x) can be derived from the standard Taylor series formula, f(x) = f(a) + f'(a)(x-a) + f''(a)/2! (x-a)^2 + f'''(a)/3! (x-1)^3 + ... where f'(a) denotes the first derivative of function f(x) at x = a, f''(a) denotes the second derivative of f(x) at x = a and so on. By noting that the first derivative of ln(x) is 1/x, it is straightforward to derive the Taylor series for ln(x).