1) Prove that if loga x = y, then lo8b x = (loga x)(logb a). Plot loga n for 1 S ns 100 when a 2, e and 10.(10-points) 2) Prove that (b) -112-n(n+ 1 )(2n+ 1 )/6 k+1) (1-x) if X Hint: Induction - Discrete Math (15-points) 3) Consider two balanced dices with each of the six faces marked 1 to 6. In one single throw of these two dice, list all the possible outcomes. Compute the average value of the outcomes. (10-points) 4) Compute the size of the problem that can be solved on a machine that takes 10-12 sec/op in one day when T(n) = 4 n, 10 n, 2n . (10-points)