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Algebra 2 Name: _________________________________

8.4 – 8.6 Quiz Review Logarithmic Functions & Their Properties ♦LEARNING TARGET – 8.4 LOGARITHMIC FUNCTIONS♦ Rewrite the following logarithmic equations in exponential form. 1. log! 25 = 2 2. log! 81 = 4 3. log!

!!"= −2

4. log! 1 = 0 5. log! 512 = 𝑥 6. log!

!!"= −3

Rewrite the following exponential equations in logarithmic form. 7. 9! = 81 8. 2!! = !

! 9. 10! = 100,000

Evaluate and simplify the common/natural logarithms. 10. log 10! 11. 𝑒!" !! 12. 10!"#!.!

13. ln 𝑒!! 14. 15!"#!" !! 15. log 1000000

16. log!8! 17. log!16! 18. log!4!

!

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Find the inverse of each equation. 19. 𝑦 = 𝑒! 20. 𝑦 = log(𝑥 − 2) 21. 𝑦 = log! 𝑥 − 4 22. 𝑦 = ln(2𝑥 + 1) 23. 𝑦 = 𝑒!! 24. 𝑦 = 4! + 1 ♦LEARNING TARGET – 8.5 GRAPHS OF EXPONENTIAL & LOGARITHMIC FUNCTIONS♦ Graph each logarithmic function. Find the y-intercept and the asymptote. Then describe how the graph is transformed from the graph of its parent function. 25. Parent: 𝑓 𝑥 = 2! 26. Parent: 𝑓 𝑥 = 2! Transformed: 𝑔 𝑥 = 2!!! Transformed: 𝑔 𝑥 = 2! − 3

Describe Transformation: Describe Transformation: Asymptote: Asymptote:

Domain: Domain: Range: Range: 27. Parent: 𝑓 𝑥 = log 𝑥 28. Parent: 𝑓 𝑥 = log 𝑥 Transformed: 𝑔 𝑥 = log(𝑥 − 2) Transformed: 𝑔 𝑥 = log 𝑥 − 2 Describe Transformation: Describe Transformation: Asymptote: Asymptote: Domain: Domain: Range: Range:

x y 0 1 1

x y 0 1 1

x y

1

1 0

x y

1

1 0

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Write each transformed function. 29. The function 𝑓 𝑥 = !

!

! is translated 4 units right, reflected across the x-axis, and vertically stretched by a

factor of 1.5. 30. The function 𝑓 𝑥 = ln 𝑥 is translated 3 units left, vertically compressed by a factor of !

! and translated 5 units

down. 31. The function 𝑓 𝑥 = 𝑒! is reflected across the y-axis and translated 1 unit right. Match each order of transformation of 𝒇 𝒙 = 𝒆𝒙 with its transformed function. 32. ____________ stretched vertically by a factor of 2 and translated 5 units down. 33.____________ stretched vertically by a factor of 2, translated 1 unit left, and translated 5 units up. 34. ____________ reflected across the x-axis, stretched vertically by a factor of 2, and translated 5 units down. 35. ____________ stretched vertically by a factor of 2, translated 1 unit to the right, and translated 5 units up. 36. ____________ reflected across the x-axis, stretched vertically by a factor of 2, translated 1 unit to the left, and translated 5 units down.

A. 𝑔 𝑥 = −2𝑒! − 5

B. 𝑔 𝑥 = 2𝑒! − 5

C. 𝑔 𝑥 = 2𝑒!!! + 5

D. 𝑔 𝑥 = 2𝑒!!! + 5

E. 𝑔 𝑥 = −2𝑒!!! − 5

MATCH the following functions to the letter of their corresponding graphs. 37. 𝑓 𝑥 = 2! − 4 38. 𝑔 𝑥 = 𝑒! + 4 39. ℎ 𝑥 = log!(𝑥 − 4)

40. 𝑚 𝑥 = !!

!− 4 41. 𝑘 𝑥 = 𝑒!!! 42. 𝑗 𝑥 = ln(𝑥 + 4)

A. B. C. D. E. F.

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♦LEARNING TARGET – 8.6 PROPERTIES OF LOGARITHMS♦ Express as a single logarithm. Simplify, if possible. 43. log! 12 + log! 18 44. log! 81 − log! 27 45. log! 128 − log! 8 46. log! 18 + log! 72 47. log! 3125 − log! 25 48. log! 128 + log! 256 49. log! 256 − log! 64 50. log! 8019 − log! 99 51. log! 5 + log! 125 Condense the following logarithms into one. 52. 5 log 𝑥 − 4 log 𝑦 53. ln 12 − ln 3 54. 5 log! 2 + 7 log! 𝑥 + 4 log! 𝑦 55. 2 log 𝑥 + log 11 56. 6 ln 2 − 4 ln 𝑦 57. 2 log 20 − log 4 + 0.5 log 4 Expand the following logarithmic expression using properties of logarithms. 58. log 4𝑥 59. log 3𝑥! 60. log !

!

61. log !

!! 62. ln 4𝑥!𝑦 63. log 9𝑥