Estimating Logarithms

While reading through the fantastic book The Lost Art of Logarithms by Charles Petzold I was nerd-sniped by a simple method of estimating the logarithm of any number base 10. According to the book, it was developed by John Napier (the father of the logarithm) about 1615. In french the natural logarithm is also called “le logarithm népérien” in reference to the mathematician. The Method We note that due to the nature of the logarithm (always referring to base 10 from here one out), the logarithm of any number N N N is approximately equal to the number of digits of N N N minus one. This is quite easy to see when thinking about numbers between 100 and 1000 for example: 100 ≤ N < 1000 log ⁡ ( 100 ) ≤ log ⁡ ( N ) < log ⁡ ( 100 ) 2 ≤ log ⁡ ( N ) < 3 \begin{align} 100 &\leq N < 1000 \\\ \log(100) &\leq \log(N) < \log(100) \\\ 2 &\leq \log(N) < 3 \end{align} 100 lo g ( 100 ) 2 ​ ≤ N < 1000 ≤ lo g ( N ) < lo g ( 100 ) ≤ lo g ( N ) < 3 ​ ​ This approximation by itself might seem useless at ... Read full article.