Solutions Extended Pratice Logarithms 16-17.pdf

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EP 5.1

1. 1.672 2. 1.505

3. −0.146

4. Error

5. 2.076

6. 1.755

7. −0.357

8. Error 9. 1 10. log ( 1

1000) = −3

11. 40 _{= 1}

12. log₅625 = 4 13. 23 _{= 8}

14. log₆(1

6) = −1

15. 9−2 ₌ 1 81

16. Log₉(729) = 3 17. log7(7) = 1

18. 35 _{= 243}

19. 7−3 ₌ 1 343

20. Log₃(27) = 3 21. 63 _{= 216}

22. 27 _{= 128}

23. log₇49 = 2 24. 75 _{= 16807}

25. log₄64 = 3 26. 3−2 ₌1

9

27. 213_{= 8192}

28. log₅25 = 2 29. log₍1

4)

64 = −3

30. 2−1 ₌1 2

31. log₍1 3)

(1

27) = 3

32. 101 _{= 10}

33. 32 _{= 9}

34. 𝑒1 _{= 𝑒}

35. log₍1 2)

4 = −2 36. log10100 = 2

37. ln 𝑚 = 𝑛

38. 26 _{= 64}

39. 𝑦8 _{= 𝑥}

40. log₂(1

8) = −3

41. ln 2 = 3𝑥 42. 𝑒0 _{= 1}

43. 𝑒6 _{= 𝑥}

44. log₁₂144 = 2 45. ln 1 = 0

EP 5.2

1. 1 2. 3 3. 0 4. 𝑥 5. 3 − 𝑥 6. 0 7. 1 8. 𝑥2

9. 10𝑥 + 5

10. 𝑥 11. 𝑥 12. 𝑥 13. 3 14. 5 15. 2 16. 1 17. 𝑥 18. 𝑥

19.≈ 2.161

20. ≈ 5.000 21. ≈ 1.976 22. ≈ 0.463 23. ≈ 3.144 24. ≈ 1.893 25. ≈ 2.365 26. ≈ −0.693 27. ≈ 0.512 28. ≈ 2.631 29. ≈ 4.025 30. ≈ 1.301 31. ≈ 1.77 32. ≈ −0.903

33. ≈ 3.822 34. ≈ 4.170 35. ≈ 2.153 36. ≈ 1.431 37. ≈ 0.431 38. ≈ 4.200 39. ≈ 1.745

EP 5.3

1. 𝑓−1_{(𝑥) = 4}𝑥

2. 𝑓−1_{(𝑥) = 10}𝑥

3. 𝑓−1_{(𝑥) =}𝑒𝑥 2

4. 𝑓−1_{(𝑥) = 𝑒}𝑥_{− 1}

5. 𝑓−1_{(𝑥) =}2𝑥 4 =

1 4∙ 2

𝑥

6. 𝑓−1_{(𝑥) = 10}𝑥_{+ 6}

7. 𝑓−1_{(𝑥) = 10}𝑥+2_{− 7}

8. 𝑓−1_{(𝑥) = 6}𝑥+3_{+ 10}

9. 𝑓−1_{(𝑥) = 𝑒}𝑥−5₂ _{− 8}

10. 𝑓−1_{(𝑥) =}3𝑥−1+4 3

11. 𝑓−1_{(𝑥) = log}

2(𝑥 − 2) + 7

12. 𝑓−1_{(𝑥) = log}

5(𝑥 − 2) + 3

13. 𝑓−1_{(𝑥) =}ln(𝑥+1)+5 4

14. 𝑓−1_{(𝑥) = log}

7(𝑥 + 3) + 2

15. 𝑓−1_{(𝑥) =}ln (𝑥+5)−4 3

16. 𝑓−1_{(𝑥) =}ln(𝑥) 3

17. 𝑓−1_{(𝑥) = log} 3(

𝑥 4)

18. 𝑓−1_{(𝑥) =}log4( 𝑥 2)

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EP 5.4

1.

Domain: (0, ∞) Range: (−∞, ∞) Asymptote: 𝑥 = 0 2.

Domain: (0, ∞) Range: (−∞, ∞) Asymptote: 𝑥 = 0

3.

Domain: (−4, ∞) Range: (−∞, ∞) Asymptote: 𝑥 = −4

6.

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9.

Domain: (−∞, 2) Range: (−∞, ∞) Asymptote: 𝑥 = 2 10.

Domain: (2, ∞) Range: (−∞, ∞) Asymptote: 𝑥 = 2

12.

Domain: (−∞, 2) Range: (−∞, ∞) Asymptote: 𝑥 = 2 13.

Domain: (−∞,5

3)

Range: (−∞, ∞) Asymptote: 𝑥 =5

3

14.

Domain: (−∞, 2) Range: (−∞, ∞) Asymptote: 𝑥 = 2

15.

Domain: (−8, ∞) Range: (−∞, ∞) Asymptote: 𝑥 = −8 16.

Domain: (−∞, 2) Range: (−∞, ∞) Asymptote: 𝑥 = 2

17. See Mrs. Mikesell Solution

EP 5.5

1. Parent function: 𝑃 (𝑥) = log₂𝑥 Description: Move right 4 units 2. Parent function:

𝑃 (𝑥) = log3𝑥

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3. Parent function: 𝑃 (𝑥) = log₄𝑥 Description: Move left 2 units Move down 5 units 4. Parent function:

𝑃 (𝑥) = log₅𝑥 Description:

Stretch by factor of 6 5. Parent function:

𝑃 (𝑥) = log₄𝑥 Description: Reflect on x-axis Right 4 units

6. Parent function: 𝑃 (𝑥) = log2𝑥

Description: Left 5 units Up 3 units Shrink by 1

3

7. Description: Up 2 units Equation:

𝑚(𝑥) = log(𝑥) + 2 8. Description:

Right 4 units Equation:

𝑚(𝑥) = ln(𝑥 − 4) 9. Description:

Left 1 unit Down 2 units Equation:

𝑚(𝑥) = log₅(𝑥 + 1) − 2 10. Description:

Reflect on x-axis Stretch by 2 Right 1.5 units Equation:

𝑚(𝑥) = − log₃(2𝑥 − 3)

11. Description: Shrink by 0.5 Reflection on y-axis Move up 1 unit Equation: 𝑚(𝑥) = 0.5 log1

2

(−𝑥) + 1 12. Description:

Right 2 units Up 2 units

Reflection on x-axis Equation:

𝑚(𝑥) = − ln(𝑥 − 2) + 2 13. 𝑐(𝑥) = log₃(𝑥 − 6) + 3 14. 𝑐(𝑥) = − log3(𝑥 − 2) − 1

15. 𝑐(𝑥) = log₃(−𝑥) − 8 16. 𝑐(𝑥) = 2 ∙ log₃(𝑥) − 1 17. 𝑐(𝑥) =3

2∙ log3(−(𝑥 + 2))

18. 𝑐(𝑥) = log3(𝑥 + 4) + 7

EP 5.6

1. 𝑥 = 343

2. 𝑥 = 4

3. 𝑥 = 10

4. 𝑥 = +9, −9

5. 𝑥 = 1

6. 𝑥 = 1

81

7. 𝑛 = −15

8. 𝑒7 ≈ 1096.633

9. 𝑥 = 5

10.𝑥 = 34

11. 𝑥 = 96 12. 𝑥 = 23 13. 𝑥 ≈ 3.893 14. 𝑥 = 2 15. 𝑥 = 8 16. 𝑥 = 4 17. 𝑥 = 8 18. 𝑥 = 72 19. 𝑥 =2

3

20. 𝑥 = +5, −5

21. 𝑥 = 1 22. 𝑥 = 4 23. 𝑥 = 7 24. 𝑥 = 4 25. 𝑥 =𝑒3

2 ≈ 4.437

26. 𝑥 ≈ 4.437 27. 𝑥 = 4, −1

EP 5.7

1. 𝑥 ≈ 2.215 2. 𝑥 ≈ 8.044

3. 𝑥 ≈ −2.320

4. 𝑥 ≈ 0.463

5. 𝑥 = 3

6. 𝑥 ≈ 5.640

7. 𝑥 = 3

8. 𝑥 ≈ 1.099 9. 𝑥 ≈ 2.253 10. 𝑥 =log(25)

log 7 + 3 ≈ 4.654

11. 𝑥 =log4(15)

3 ≈ 0.651

12. 𝑥 =ln(12)

3 ≈ 0.828

13. 𝑥 = ln(6) + 1 ≈ 2.7918 14. 𝑥 ≈ 10.840

15. 𝑥 = 5 − log415 ≈ 3.047

16. 𝑥 ≈ 1.052 17. 𝑥 =ln(9)

2 ≈ 1.099

18. 𝑥 =log4(11)+6

3 ≈ 2.577

19. 𝑥 ≈ 2.129 20. 𝑥 = 2 21. 𝑥 =log5(7)−1

2 ≈ 0.1045

22. x = ln(16) + 1 ≈ 3.773 23.𝑥 =log2(72)

5 ≈ 1.23398

24. 𝑥 = log9(772) ≈ 3.026

EP 5.8

1. log57 + log5𝑥

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4. log67 + 3 log6𝑥

5. log 𝑥 − log 7 6. log₂𝑚 + 3 log₂𝑛 7. 2 log₂𝑥 + 5 log₂𝑦 8. 8 log₄𝑥 − log₄5 9. ln 𝑒 + ln 𝑥 → 1 + ln 𝑥 10. Ln 1 − ln 𝑥 → 0 − ln 𝑥 →

− ln 𝑥

11. Ln 2 + 3 ln 𝑥 + 2 ln 𝑦 12. 2 log 𝑚 + 5 log 𝑛 13. (log 𝑥 + log 𝑦) − log 5 14. (log73 + 4 log7𝑥) − log7𝑦

15. 5 log₄𝑥 + 7 log₄𝑦

16. 2 + log₇𝑥 + log₇𝑦 + log₇𝑧 17. 4 log₂7 + 4 log₂𝑥 →

4(log27 + log2𝑥)

18. log(2𝑥 + 1) + log(𝑥 + 7) 19. (2 ln 𝑎 + 3 ln 𝑏) − 4 ln 𝑐 20. 3 log 𝑚 − 4 log 𝑛 +

2 log 𝑝 → (3 log 𝑚 + 2 log 𝑝) − 4 log 𝑛

21. Ln 27 − (2 ln 𝑥 + 5 ln 𝑦) 22. log₂(𝑥2 _{− 4) − 3 log}

2𝑥

23. 2 ln 𝑥 − (5 ln 𝑦 + 3 ln 𝑤) 24. 𝑐

25. 2 ln 𝑥 26. ln 𝑐 − ln 3

EP 5.9

1. 2 2. 4 3. 3 4. 0 5. 1 6. −2 7. 1 8. 2 9. 2 10. 5 11. log₂𝑥5 12. log (2𝑥

3𝑦)

13. log₃(𝑥2

𝑦)

14. ln(2𝑥) 15. ln 𝑥3

16. ln(7𝑥) 17. log (2𝑥+5

𝑥−3)

18. ln 𝑥8

19. Log6( 𝑥5𝑦2

𝑧

2 3

)

20. Log (𝑥𝑦3 𝑧

1 2

)

21. Log (7𝑥(𝑥2−1)

𝑥+1 ) = log(7𝑥(𝑥 −

1)) 22. ln ( 𝑥−2

𝑥3_(𝑥2₋₄₎) = ln (

1 𝑥3_(𝑥+2))

23. ln ((2𝑥+3)2

(𝑦−2)4)

24. log₃(𝑥5

𝑦5)

EP 5.10

1. 𝑥 = 6

15

2. 𝑥 = 4

3. 𝑥 = 4 4. 𝑥 = 8 5. 𝑥 = 77 6. 𝑥 = 12 7. 𝑥 = 25 8. 𝑥 = 12 9. 𝑥 = 6 10. 𝑥 = 10 11. 𝑥 = 0, 𝑥 =

−6 𝑒𝑥𝑡𝑟𝑎𝑛𝑜𝑢𝑠 𝑠𝑜𝑙𝑡𝑢𝑖𝑜𝑛 12. 𝑥 = 27

13. 𝑥 = 4 14. 𝑥 =1

3

15. 𝑥 = 3 16. 𝑥 = 2, −1 17. 𝑥 = 5, −3 18. 𝑥 = −9, 4 19. 𝑥 = 2, −8 20. 𝑥 = 16, −4 21. 𝑥 = 4, −20

EP 5.11

1. 𝑅𝑜𝑓𝐶 =1

9

2. 𝑅𝑜𝑓𝐶 = 24

3. 𝑅𝑜𝑓𝐶 ≈ 3.98

4. 𝑅𝑜𝑓𝐶 ≈ −0.275

5. 𝑅𝑜𝑓𝐶 ≈ 0.92419

6. 𝑅𝑜𝑓𝐶 = 127.5

7. 𝑅𝑜𝑓𝐶 = −1

4

8. 𝑅𝑜𝑓𝐶 = −3

7

9. 𝑅𝑜𝑓𝐶 = 1.55

10. Answers will vary 11. 𝑅𝑜𝑓𝐶 = −4 12. 𝑅𝑜𝑓𝐶 = −7

3

13. 𝑅𝑜𝑓𝐶 = 3 14. 𝑅𝑜𝑓𝐶 = 1

2

15. 𝑅𝑜𝑓𝐶 = −1 3

16. 𝑅𝑜𝑓𝐶 = 2