 Binary logarithms also occur in the exponents of the time bounds for some divide and conquer algorithms , such as the Karatsuba algorithm for multiplying n @-@ bit numbers in time O ( nlog2 3 ) , and the Strassen algorithm for multiplying n × n matrices in time O ( nlog2 7 ) . The occurrence of binary logarithms in these running times can be explained by reference to the master theorem . 
