TASK 2: INDEX RULES (1) Simplify the following expressiony applying the index rules. Only apply one rule at each step and identify the rule you applied. (a) 12243 - 424 (b) "F + (4x3)2 (b) 2p10_3x2 (2) Solve the following expression for a: 13x- = 39. TASK 3: LOG RULES (1) Simplify the following expressions by applying the log rules. At each step identify the rule you applied. (a) logs(4) + logs(2) (b) 2log2(12) - log2(4) (2) Use a change of base, then simplify to express logis (60) 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) In(2 + 3) = 7 (b) elx-7 = 8 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 a + = = 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 r + 2 = 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?SIT190 - PAGE - WEEK 5 - ONTRACK ASSESSMENT 3 TABLE 1. Heap-calculation: a + $ = 19 Steps Example A guess is made. Guess is r = 7 The left hand side (LHS) is evalu- LHS= + = = 7+ ; ated with the guess value. =7+1 =8 If the LHS does not equal the right As LHS=8 and RHS=19, hand side (RHS), we divide the RHS we get 19 by the LHS We now multiply our guess by this a = 7 x 19 133 8 number to obtain the correct value for r Checking: when r = 133 8, we have r + 133 1 133 X 1064 = 19 56