Math Logarithms Test Review Blank

Algebra 2 Honors Let ( ) = when necessary. 1. ( (6)) Name________________ Date_________________ Logs Test Review ( )=√ ( )= . Perform the indicated operation and state the domain 2. ( ( 3)) 3. ( (6)) 4. ( ( )) 5. ( ( )) 6. ( ( )) 7. ( ( )) 8. ( ( )) 9. ( ( )) Without Graphing, determine whether or not the following functions have inverse functions. ( )= ( )=2 ( ) = 5 + 17 10. + 17 11. 18 + 12. 8 Find the following inverse functions, if they exist. 13. ( )= +7 14. ( )= +8 15. ( ) = 2( + 5) Find the inverse function for each of the following. 16. ( ) = log + 7 17. ( ) = 18. ( ) = log ( + 5) Evaluate each of the following logarithms. 19. log 27 20. log √27 21. log 4√32 22. log Solve each of the following equations, if a solution exists. 23. log = 24. log = 25. log 27 = Condense the following logarithmic expressions into a single logarithm. 27. 4 2 log 28. 2 log log Simplify the following logarithmic expressions. 29. log + 3 + log 2 30. , 26. log 125 = 3 (2 log 4 + 2 log 2) log 2 Solve the following logarithmic equations. Check for extraneous solutions. Round answers to the nearest thousandth. 31. 3 + 2 ln = 10 32. log (3 ) = log 3 + log log ( 33. log 35. log(10 ) 34. log (2 1) = log 2 + √ =1 36. ln( 5) log (7 + 10) = 1) + ln( + 2) = 1 Solve the following exponential equations. You must have an exact answer. 37. 25 = 25 38. 81 = √27 Solve the following exponential equations. Round answers to the nearest thousandth. 39. = 12 40. 4 =7 41. 12 = 5 1 42. 4 + 3 45. 2 =8 43. 2 =0 46. 4 =4 44. 100(1.04) 3 =0 47. = 300 +4 21 = 0 48. A man invests $5,000 in an account that pays 8.5% interest per year, compounded quarterly on July 1, 2008. a. Find the amount after 3 years. b. During which month of what year will the amount double? 49. A man invests $6,500 in an account that pays 6% interest per year, compounded continuously. a. What is the amount after 2 years? b. How long will it take for the amount to be $8,000? 50. During which month of what year will it take for an investment of $1,000 deposited on February 1,1998 to double in value if the interest rate is 8.5% per year, compounded continuously? 51. A sum of $1,000 was invested for 4 years, and the interest was compounded semiannually. If this sum amounted to $1,435.77 in the given time, what was the interest rate? 52. A culture contains 1,500 bacteria initially and doubles every 30 minutes. a. Find a function that models the number of bacteria at time . b. Find the number of bacteria after two hours. c. After how many minutes will there be 4,000 bacteria? 53. Radium-226 has a half-life of 1,600 years. Suppose a sample of this substance has a mass of 22 mg. a. Find a function that models the amount of the sample remaining at time . b. Find the mass remaining after 4,000 years. c. How long will it take for the sample to decay to a mass of 18 mg? 54. Cesium-137 has a half-life of 30 years. Suppose a sample of this substance has a mass of 10 g. a. Find a function that models the amount of the sample remaining at time . b. Find the mass remaining after 80 years. c. How long will it take for the sample to decay to a mass of 2 g? Without using a calculator, graph the exponential equation ( ) = . Then, graph each of the transformed functions. Be sure to list all transformations in the order in which they must be graphed. Then, find the Domain and Range. ( )= 2 +4 56. Domain: Range: 57. ( )=2 2 Domain: Range: Without using a calculator, graph the exponential equation ( ) = . Then, graph each of the transformed functions. Be sure to list all transformations in the order in which they must be graphed. Then, find the Domain and Range. 58. ( )= Domain: Range: 59. ( )=3 1 2 6 Domain: Range: Using a Graphing Calculator, graph the following exponential equations. Then, find the Domain and Range. ( )= 2 60. +1 Domain: Range: Without Graphing, identify the Domain and Range of each of the following functions. Simple sketches may help!!!! ( )= 3 61. +7 62. ( ) = 3 4 6 Without using a calculator, graph the logarithmic function ( ) = log Then, graph each of the transformed functions. Be sure to list all transformations in the order in which they must be graphed. Then, find the Domain and Range. 4) Domain: 63. ( ) = 2log ( Range: 64. ( )= log +4 Domain: Range: Without using a calculator, graph the logarithmic function ( ) = log Then, graph each of the transformed functions. Be sure to list all transformations in the order in which they must be graphed. Then, find the Domain and Range. ( ) = log ( + 6) 65. Domain: Range: 66. ( ) = 3 log 5 Domain: Range: Using a Graphing Calculator, graph the following exponential equations. Then, find the Domain and Range. ( ) = 3ln( 6) 67. Domain: Range: Without Graphing, identify the Domain and Range of each of the following functions. Simple sketches may help!!!! 68. ( ) = 14log ( + 9) 69. ( ) = log ( + 19) 70. ( ) = log 4 Write an exponential function y  ab 72. (1, 4) and (2, 16) 71. x ( )= 3log ( 8) + 2 whose graph passes through the given points. 73. (1, 6) and (4, 162) ANSWERS (6) = 1 1. 2. ( ) =9 5. 7. ( ) =√ 9. ( ) = 14. ( )= 18. ( )=6 ( 3) = √10 3. (6) = : ( ∞, ∞) 6. ( ) = 36 + 36; : ( ∞, √5 ∪ 5; √ ; 5, ∞) : [5, ∞) 15. 5 10. ( )= = =9 31. = 33.115 32. (0, ∞) 35. =4 36. 39. = 0.162 43. = 2.442 47. = 0.549 26. = ( ) = ( ) = 4. ; : ( ∞, 9] ; : [0, ∞) ±√ 11. 5 19. 24. 25. 8. 10 12. 20. 21. 27. log 28. log 17. 4 22. √ 29. 0 23. ( ) = ln + 4 = 2 √2 30. 34. =2 34. =8 = 1.729 37. = 38. =0 40. = 0.280 41. = 7.353 42. = 0.252 44. = 14.006 45. = ±1 46. = 0, 48a. $6,435.09 49b. 3.46 50. 52b. 24,000 52c. ≈ 42.5 53c. 463.21 54a. = 10 2016 48b. 2006 51. ≈ 9.25% 53a. = 22 = 1500(2) 53b. 3.89 54b. 1.57 54c. 69.7 : ( ∞, ∞) : ( ∞, 4) 57. : ( ∞, ∞) : (0, ∞) 58. : ( ∞, ∞) : ( ∞, 0) 59. : ( ∞, ∞) : ( 6, ∞) 60. : ( ∞, ∞) : ( ∞, 1) 61. : ( ∞, ∞) : ( ∞, 7) 62. : ( ∞, ∞) : ( 6, ∞) 63. : (4, ∞) : ( ∞, ∞) 64. : (0, ∞) : ( ∞, ∞) 65. : ( 6, ∞) : ( ∞, ∞) 66. : (0, ∞) : ( ∞, ∞) 67. : (6, ∞) : ( ∞, ∞) 68. : ( 9, ∞) : ( ∞, ∞) 69. : ( 19, ∞) 70. : (0, ∞) : ( ∞, ∞) 71. : (8, ∞) 72. = 1(4) 73. = 2(3) : ( ∞, ∞) 49a. $7,328.73 52a. 56. : ( ∞, ∞) : [5, ∞) 13. ( )=3 16. 5;