Prove the following theorems using the definition of Big-Oh:

R5: If f(n) ao + aln + + adnd, d and a, are constants, then f (n) is O(n") R6: nx is 0(an) for any fixed x 0 and a 1 R7: log(n*) is 0(log n) for any fixed x 0 R8: log*n is O (n) for any fixed constants x > 0 and y > 0 23