Compare the following pairs of functions in terms of order of magnitude. In each case, say whether f(n) = O(g(n)), f(n) = (g(n)) and/or f(n) = (g(n)). Note that in each case either one or all three of these possibilities can hold (do you see why only one or three possibilities can hold ?).

f(n)................. g(n)

a. 100n + log n................ n + (log n)^2

b. log n ...............log(n^2 )

c. n^2/log n................... n(log n)^2

d. n^1/2 ...................(log n)^5

e. log_2 n .................log_1000 n

f. 2^n ...................3^n