2. [50 points] Prove the following. Assume that the log function has base 2 unless explicitly...

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2. [50 points] Prove the following. Assume that the log function has base 2 unless explicitly mentioned otherwise. log lognlogn < log < 2 logn < (2)logn n < nlogn < n/2 < 3logn < 3log(3/2)" < (n + 2") < (n log log n)! 2. [50 points] Prove the following. Assume that the log function has base 2 unless explicitly mentioned otherwise. log lognlogn < log < 2 logn < (2)logn n < nlogn < n/2 < 3logn < 3log(3/2)" < (n + 2") < (n log log n)!