 The powers of two have been known since antiquity ; for instance they appear in Euclid 's Elements , Props . IX.32 ( on the factorization of powers of two ) and IX.36 ( half of the Euclid – Euler theorem , on the structure of even perfect numbers ) . And the binary logarithm of a power of two is just its position in the ordered sequence of powers of two . On this basis , Michael Stifel has been credited with publishing the first known table of binary logarithms in 1544 . His book Arthmetica Integra contains several tables that show the integers with their corresponding powers of two . Reversing the rows of these tables allow them to be interpreted as tables of binary logarithms . 
