Convert the following expressions between exponential and logarithmic form. a. 2401 = 74 [1 mark] b. ???? = logb ???? [1 mark] Solve for ????. Give your answer to three decimal places where appropriate. a. ???? = log 21 [2 marks] b. ???? = log22 10 000 [2 marks] c. 2???? = 23 [2 marks] d. ????9 = 1024 [2 marks] e. 5 = log???? 25 [2 marks] f. 3.5 = log36 ???? [2 marks] Use the properties of logarithms to solve the following equations. a. b. c. ???? = log11(1121) [1 mark] 4log4(57) = ???? [1 mark] ???? = log100 1000 [1 mark] Solve for the unknown using a method of your choice. a. 511????+23 = 1257???? [3 marks] b. 2???? = 123 [3 marks] c. 3????+5 + 3???? = 177876 [3 marks] Describe the transformations on the logarithmic function ????(????) = [6 marks] Write the equation of a logarithmic function that has been vertically stretched by 4, reflected in the x-axis, horizontally compressed by 1/9, moved 11 units up and 12 units left. Justify your answer. [4 marks] Ethan bought a new car worth $54,000. After 5 years, the car was worth $28,497.52. Calculate the annual depreciation rate of Ethan's car. [3 marks] The hydrogen ion concentration of a lemon is about 0.02. What is its pH? [2 marks] How do the intensities of a magnitude 6.0 earthquake and a magnitude 2.9 earthquake compare? [3 marks] 10. Using logarithm properties there are multiple ways of expressing the same transformations on a parent function. Given ????(????) = 8 log[2(????)], find equivalent functions in the following forms. Round values to 4 decimal places whe