 The modern form of a binary logarithm , applying to any number ( not just powers of two ) was considered explicitly by Leonhard Euler in 1739 . Euler established the application of binary logarithms to music theory , long before their more significant applications in information theory and computer science became known . As part of his work in this area , Euler published a table of binary logarithms of the integers from 1 to 8 , to seven decimal digits of accuracy . 
