This assignment is out of 24 marks. To earn full marks for each question, a detailed algebraic solution and/or explanation is required. Review the "Directing Words" chart found in the course introduction. Complete all questions before submitting this assignment for grading. Please contact your teacher if you have any questions. 1. Convert each exponential equation to a logarithmic equation. The logarithmic equation for part b should not include the radical sign. (2 marks) a. 3* =81 b. x =V6 2. Solve by converting to exponential form. (2 marks) a. logs x =-3 b. log 32 =5 3. Given the function f (x) = 3*-2 a. Graph f (x) and f-(x) showing a minimum of two exact points for each function. Clearly label each curve and also show and label the line of reflection. (2 marks)b. Given f (x) = 3*-2 algebraically determine the equation for f- (x). (1 mark) c. Describe the transformation using a mapping statement. (1 mark) 4. The function y = log2 x is transformed to the function y = -310g2 (-- (x+ 2) ) -5. a. Use the transformation statement y = alog. (b(x-h) ) + k to complete the chart below. (3 marks) Parameter | Mapping Statement Transformation Description a =-3 ( x, V ) - (x, - 3y) Vertical stretch by a factor of 3 and a reflection across the line y=0 (the x-axis). b = h= k =b. Sketch the graph of y = -310g2 - (x+2) ) -5. (1 mark) W5. Laws of Logarithms a. Use the laws of logarithms to express as a single logarithm and then evaluate (2 marks) log2 14 + log2 4-310g2 3/7 b. Use the laws of logarithms to express as a single logarithm and then simplify. Also, determine the restriction for x. (2 marks) 2logs (x-2) -10gs (x2 - 5x +6)Vista Virtual School Math 30-1 Assignment 4 Summer 2022 6. Algebraically determine the exact solution to 3*-2 = 5*+ . State as one fraction (2 marks) 7. Algebraically determine the exact solution to log. (x -8) = 2-log. (x+ 8) (2 marks) 58. Keith makes an investment of $5000 into an account which pays an interest rate of 3.5% per year, compounded monthly. 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 triple. (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 378 and not 377. (0.5 mark) 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; I 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 triple. Show your work by completing the statements below for your graphing calculator steps. Explain how this answer verifies your results from part a. (1.5 marks) 12 = t =