Download Natural Logs and "e"

Name
7-6
Class
Date
Practice
Form G
Natural Logarithms
Write each expression as a single natural logarithm.
4. ln z  3 ln x
5.
1
ln 9 + ln 3x
2
6. 4 ln x + 3 ln y
Solve each equation. Check your answers. Round your answer to the nearest
hundredth.
10. 4 ln x = 2
11. 2 ln (3x  4) = 7
12. 5 ln (4x  6) = 6
16. 2 ln x + ln x2 = 3
17. ln x + ln 4 = 2
18. ln x  ln 5 = 1
22. ln 3x + ln 2x = 3
23. 5 ln (3x  2) = 15
24. 7 ln (2x + 5) = 8
Use natural logarithms to solve each equation. Round your answer to the
nearest hundredth.
28. ex = 15
29. 4ex = 10
36. 3e3x5 = 49
37. 7e5x+8 = 0.23
30. ex 1  = 50
38. 6  e12x = 5.2
53
31. 4e3x21 = 5
x
39. e 5  25
Lesson 7-4
Write each expression as a single logarithm.
44. log 8 + log 3
45. 4(log2 x + log2 3)
46. 3 log x + 4 log x
47. log 4 + log 2  log 5
Expand each logarithm.
48. logb 2x2y3
51. log b
x2
2y
49. logb 3m3p2
52. log b
( xy ) 4
2
50. logb (4mn)5
53. logb
5
x3
Lessons 7-5 and 7-6
Solve each equation.
x
59. log3 (x + 1) = 4
60. ex = 5
61. e 4 = 5
62. ln x  ln 4 = 7
63. log 4x = 1
64. log 4  log x = 2
65. ln 2 + ln x = 4
66. 4 + 5x = 29
67. e3x = 20
Simplify each expression.
68. 5 ln 1
71.
ln e
3 ln e3
69. ln e2
70.
1
ln e 20
72. 2 ln e5
73.
3ln e 4
2 ln e 6