Please hand draw these answers

TASK 2: INDEX RULES (1) Simplify the following expressions by applying the index rules. Only apply one rule at each step and identify the rule you applied. (a) (53)2 (b) (53)25-2 - 535 (c) (Clue: use technique for removing negative powers given in the workshop.) (2) Solve the following expression for c: 9r = 81.TASK 3: LOG RULES (1) Simplify the following expressions by applying the log rules. At each step iden- tify the rule you applied. 2 Trimester 1. 2023 (a) logis (3) + log15(5) (b) log, (18) - 2 log. (3) (2) Solve the following expressions for r: (a) In(2x) = 4 (b) (2z = 4