Questions:

Solve each of the following recurrences using the Master Theorem: state which case is applicable, state the value of a and b and f(n), and show that the recurrence satisfies the conditions of the case. If the Master Theorem does not apply, state this; you do not have to solve the recurrence using other methods.

1. T(n) = 5T(n/3) + n log n
2. T(n) = 3 T(n/3) + n/log n
3. T(n) = 81 T(n/9) + n²
4. T(n) = 81 T(n/9) + n log log n
5. T(n) = 81 T(n/9) + n² log n
6. T(n) = 2T(n/3) + n