How to calculate $\ln(17)$ without calculator? Hi I've been playing with ln(Natural logarithm) since I first learn it in physic class and my goal is to calculate it without using the calculator. I done $$\ln(12,14,15,16,18,\ldots)$$ just fine but for $$\ln(17,13,11)$$ I can't seen to divide them into anything other than $\ln(17)=(17\cdot1).$ I was wondering if there's a method to do this? Thank you :D

You might try $\ln(17)=\ln(16)+\int_{16}^{17} \frac1x dx$.

You can then estimate the integral as a rectangular area with width $1$ and height $\frac{1}{16.5}$.

This gives $\ln(17)\approx \ln(16)+\frac{2}{33}$

According to my calculator, $\ln(17)\approx 2.83321334$, and $\ln(16)+\frac{2}{33}\approx 2.833194783$.

For better accuracy, you could partition $[16,17]$ into two (or more) subintervals.