Mathematical constant
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.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e13c1be02315217e5bc5f20f64905a7d2539df2f)
The logarithm of 2 in other bases is obtained with the formula
![{\displaystyle \log _{b}2={\frac {\ln 2}{\ln b}}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f98fb884955db7aa25e43bc4edabdefce5334651)
The common logarithm in particular is (OEIS: A007524)
![{\displaystyle \log _{10}2\approx 0.301\,029\,995\,663\,981\,195.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f5cff2c85eb70732ff035c04e16e3c92c63ef5dc)
The inverse of this number is the binary logarithm of 10:
(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.