2. Algebraically determine the exact solution to 3* = 5"-. State as one fraction. (2 marks) 3. Algebraically determine the exact solution to log; (x -4) = 2-10g3 (x + 4) (2 marks)4. Keith makes an investment of $3000 paying at an interest rate of 7.5% per year, compounded quarterly. a. One form of the compound interest formula is A = P(1 +i)", where A is the amount of money at the end of the investment; P is the principal amount deposited; i is the interest rate per compounding period; and n is the number of compounding periods. Use the above formula to algebraically determine the number of compounding periods it would take for the investment to double. (Hint: Review page 362 in the textbook to help you set up this equation and then solve using the logarithmic laws.) State your value for n to one decimal place. (2 marks) b. Explain why the correct solution for the number of compounding periods is 38 and not 37. (0.5 mark) c. Another form of the compound interest formula is A = P(1+-) , where A is the n amount of money at the end of the investment; P is the principal amount deposited; r is the interest rate per year; n is the number of compounding periods a year; and t is the total time in years. Using this second formula graphically determine the time in years it would take for the investment to double. Show your work by completing the statements below for your graphing calculator steps. Explain how this answer verifies your results from part a. (Hint: There are 3 months in each compounding period.) (1.5 marks) MI = V2 = t =1. Laws of Logarithms a. Use the laws of logarithms to express as a single logarithm and then evaluate (2 marks) log2 6-1082 3+210g2 V8 b. Use the laws of logarithms to express as a single logarithm and then simplify. Also, determine the restriction for x. State the restriction as the values that are allowed for x. (2 marks) 210gs (x - 3) -1085 (x2 -x-6)