1. Convert the following expressions between exponential and logarithmic form. a. 2401 = 7 4 [1 mark] b. = logb [1 mark] 2. 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] 3. Use the properties of logarithms to solve the following equations. a. = log11(1121) [1 mark] b. 4 log4 (57) = [1 mark] c. = log100 1000 [1 mark] 4. Solve for the unknown using a method of your choice. a. 5 11+23 = 1257 [3 marks] b. 2 = 123 [3 marks] c. 3 +5 + 3 = 177876 [3 marks] 5. Describe the transformations on the logarithmic function () = 1 2 log [ 1 7 ( 2)] + 9 [6 marks] 6. 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] 7. 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] 8. The hydrogen ion concentration of a lemon is about 0.02. What is its pH? [2 marks] 9. 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 where appropriate. a. () = log() + [3 marks] b. () = log[()] [3 marks] c. () = log[( )] [3 marks] 11. Not all logarithmic and exponential equations can be solved algebraically. Use technology to solve the equation 3 23 = log2 (2) to 4 decimal places. Include a sketch MHF4U Learning Activity 2.6 Unit 2 Assignment Copyright 2022 The Ontario Educational Communications Authority. All rights reserved. 2 TVO ILC or screenshot in your solution. [5 marks] 12. Why must the base of a logarithm be positive? [3 marks] 13. Why can we not calculate the logarithm of a negative number? [3 marks] 14. Rod says that he is thinking of a one variable exponential or logarithmic equation that has the following characteristics: a. has solutions = 1 and = 2 b. does not contain the digit "3" c. contains the number -12. What are two different equations that Rod could be thinking of? Are those the only possible answers? [6 marks] 15. Solve, rounding final answers to three decimals where appropriate, 5 5 = 2(6 22 ) [5 marks] 16. Solve, rounding to three decimals where appropriate, log4 (3 + 1) = 2 [5 marks]