College Algebra, 2013a

6.1 Introduction to Exponential and Logarithmic Functions 433
6.1.2 Answers
1. log 2 (8) = 3 2. log 5
( 1
125)
= −3 3. log4 (32) = 5 2
(
4. log 1 (9) = −2 5. log 5
)
4
3
25 2 = −
1
2
6. log(0.001) = −3
7. ln(1) = 0 8. 5 2 =25 9. (25) 1 2 =5
10. 3 −4 = 1
81
11. ( )
4 −1
3 =
3
12. 10 2 = 100
4
13. 10 −1 =0.1 14. e 1 = e 15. e − 1 2 = 1 √ e
16. log 3 (27) = 3 17. log 6 (216) = 3 18. log 2 (32) = 5
19. log 6
( 1
36)
= −2 20. log8 (4) = 2 3
21. log 36 (216) = 3 2
22. log 1 (625) = −4 23. log 1 (216) = −3 24. log 36 (36) = 1
5
6
25. log
1
1000000 = −6 26. log(0.01) = −2 27. ln ( e 3) =3
28. log 4 (8) = 3 2
29. log 6 (1) = 0 30. log 13
(√
13
)
=
1
2
31. log 36
( 4
√
36
)
=
1
4
32. 7 log 7 (3) = 3 33. 36 log 36 (216) = 216
(
34. log 36 36
216 ) (
= 216 35. ln(e 5 )=5 36. log
( )
( )
3√
37. log 10 5 = 5 3
38. ln 1√e
= − 1 2
)
9√
10 11 = 11
9
39. log 5
(
3
log 3 5 ) =1
40. log ( e ln(100)) = 2 41. log 2
(
3
− log 3 (2) ) = −1 42. ln ( 42 6log(1)) =0
43. (−∞, ∞) 44. (−2, ∞) 45. (5, ∞)
46. (−∞, −6) ∪ (−3, ∞) 47. (−2, −1) ∪ (1, ∞) 48. (−6, −3) ∪ (5, ∞)
49. (4, 7) 50. (5, ∞) 51. (−∞, ∞)
52. [1, ∞) 53. (−∞, −7) ∪ (1, ∞) 54. (13, ∞)
55. (0, 125) ∪ (125, ∞) 56. No domain 57. (−∞, −3) ∪ ( 1
2 , 2)