Natural logarithm of 2

The decimal value of the natural logarithm of 2 (sequence A002162 in the OEIS) is approximately

${\displaystyle \ln 2\approx 0.693\,147\,180\,559\,945\,309\,417\,232\,121\,458.}$

The logarithm of 2 in other bases is obtained with the formula

${\displaystyle \log _{b}2={\frac {\ln 2}{\ln b}}.}$

The common logarithm in particular is (OEIS: A007524)

${\displaystyle \log _{10}2\approx 0.301\,029\,995\,663\,981\,195.}$

The inverse of this number is the binary logarithm of 10:

${\displaystyle \log _{2}10={\frac {1}{\log _{10}2}}\approx 3.321\,928\,095}$ (OEIS: A020862).

By the Lindemann–Weierstrass theorem, the natural logarithm of any natural number other than 0 and 1 (more generally, of any positive algebraic number other than 1) is a transcendental number.