I'm developing my own Real Number class in Python for my projects. In that class, user can store or access $ n \in \mathbb{N} $ number of digits after the decimal point.
Everything is completed, except the power function. I want to calculate the power using natural logarithm. I'm learning mathematics now, but unfortunately, currently I haven't cover real analysis. But I need help from that field.
I'm using Taylor's series of natural logarithm. But I want the natural log series for any x greater than 1 also.
Can anyone guide me to the right (and easy, if possible) path to implement the natural log series?
And one more query - user can select up to how many digit he/she wants in answer after the decimal point. So, to get n number of digits accurately after the point, how many terms I need to take in the series? Does there any general formula exist?