Mock AIME 5 Pre 2005 Problems/Problem 15

We need to find $[log_2{53}]+[log_2{54}]+[log_2{55}]+...+[log_2{64}]$ , and since $2^{\frac{11}{2}}=\sqrt{2048}<46$ , and we have $[log_2{53}]=[log_2{54}]=[log_2{55}]=...=[log_2{64}]=6$ , and the answer is $6\times12=\boxed{72}$ . ~AbbyWong