 The running time of an algorithm is usually expressed in big O notation , which is used to simplify expressions by omitting their constant factors and lower @-@ order terms . Because logarithms in different bases differ from each other only by a constant factor , algorithms that run in O ( log2 n ) time can also be said to run in , say , O ( <unk> n ) time . The base of the logarithm in expressions such as O ( log n ) or O ( n log n ) is therefore not important and can be omitted . However , for logarithms that appear in the exponent of a time bound , the base of the logarithm cannot be omitted . For example , O ( <unk> n ) is not the same as O ( <unk> n ) because the former is equal to O ( n ) and the latter to O ( <unk> ... ) . 
