TRIM ESTER. 3. 2022 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) 12243 424 l": '1 (h) I??? + (4973? {2) Solve the following expression for 3:: 13;"-2 = 39. TASK 3: LOG RULES {1) Simplify the following expressions by applying the log rules. At each step identify the rule you applied. (a) loss) + loam (h) og-gum log-2(4) {2) Use a change of base, then simplify to express log15(} as a fraction. (You must select a base which means you do not have to use a calculator to get the solution.) {3) Solve the following expressions for :r: (a) ln{:r + 3} = 7 TASK 4: CULTURAL CONTRIBUTION A paper on the Mathematics of Ancient Egypt by J. Dubbey is available at https: //www. jstor. org/stable/30211437. There are further references in the unit site - see 'Interesting snippets' under the weekly content. An example of the Egyptian method of solving + = = 14 using 'heap-calculation' is given in Dubbey's paper. The method is given in Table 1. (1) Describe an application in Ancient Egypt that would require mathematics. (2) Explain why mathematics was needed in this application. (3) Solve the equation + ? = 11 using the Egyptian method of 'heap-calculation' and a guess of r = 8. (An example of this method is described in Table 1.) (4) Solver+= = 16 using our current algebraic methods. Compare the two methods. (5) Which method did you prefer and why