 For a general positive real number , the binary logarithm may be computed in two parts . First , one computes the integer part , <formula> ( called the characteristic of the logarithm ) . This reduces the problem to one where the argument of the logarithm is in a restricted range , the interval [ 1 @,@ 2 ) , simplifying the second step of computing the fractional part ( the mantissa of the logarithm ) . For any x > 0 , there exists a unique integer n such that 2n ≤ x < 2n + 1 , or equivalently 1 ≤ 2 − nx < 2 . Now the integer part of the logarithm is simply n , and the fractional part is log2 ( 2 − nx ) . In other words : 
