ln2 value is _math.c (cpython)

[Gribouillis]

You can get more decimals with the decimal module

>>> Decimal.from_float(log(2))
Decimal('0.69314718055994528622676398299518041312694549560546875')

which shows that the hard-coded value was indeed the decimal value of the ieee-754 number rounded to a higher order. I agree that it is strange.