HELP ANSWER ALL PLEASE!

1. Simplify the following: log2 ry2 log2 2 -2 log2 log2(16z2) log3(9z4)-log3 (3)2 O82 y 2. Solve for x: log2 = 5 3. Evaluate: (5v4 4. Solve the following: (-n) r-0 10 5. Prove that: ( 6. Rewrite the following expression into its closed form (i.e. without the sigma): .,2+i). 7. For each of the following, give an exact formula T(n) for the number of times //op is run: (assume -1 i+-1 each iteration unless otherwise specified) Ex. for i -1 to n do // constant time operation 6. Rewrite the following expression into its closed form (ie, without the sigma): -1(2+i). 7. For each of the following, give an exact formula T(n) for the number of times //op is run: (assume i+-1 each iteration unless otherwise specified) T(n)n for i-1 to n do Ex. // constant time operation for i- 1 to 4n do // constant time operation for i- 1 to n*n*n do // constant time operation for i 1 to 4n do for j-1 to i do // constant time operation for i-1 to n*n do for j-1 to i do // constant time operation for i1 to n do for j 1 to n do for k- 1 to n do // constant time operation for(int i-0; i 1; i/-2) // constant time operation 8. Rank the following functions by their asymptotic growth rate in ascending order. In your solution, group those functions that are big-Theta of one another (all log functions are base 2): 6 nlogn 2100 log lognog2ng n of the above. If it is none of the above, try to reason what type of curve it may be. f(0) 6, f (10)-8, f(20) 10 f(0) 80, f(0.1) 60, f(0.2) 45 .f(1) 10, f(10) 20,f(100) 30 . f(0) 2, f(3) 12, f(5) 240<>