In short, how do calculators work out what the natural log of a number is? I have read that the infinite sum:
Code:
ln(1+x) = x - x^2/2 + x^3/3 - x^4/4 + x^5/5 - x^6/6 + ...
Will produce the answer. It does but if the number is higher than 1000 the accuracy is rubbish, even if the infinite sum is calculated to its 70000th iteration.

So how does the common scientific calculator do it to such a good accuracy and so fast?