What is the best way to calculate log without a calculator? As the title states, I need to be able to calculate logs (base $10$) on paper without a calculator.
For example, how would I calculate $\log(25)$?

Use the power series $ln(y) = -ln(1-x) = \sum_{k=1}^{\infty}\frac{x^k}{k}$ with $y=\frac{1}{1-x}$. For x<1 or y>1 respectively the sum converges.
To get to a different base like 10 use the relation $log_n(x) = \frac{ln(x)}{ln(n)}$
