346 Basic Engineering Mathematics
5. x = 2, y = 4, z = 5 6. x = 1, y = 6, z = 7
7. x = 5, y = 4, z = 2 8. x = −4, y = 3, z = 2
9. x = 1.5, y = 2.5, z = 4.5
10. i 1 = −5, i 2 = −4, i 3 = 2
11. F 1 = 2, F 2 = −3 F 3 = 4
Chapter 14
Exercise 54 (page 104)
1. 4 or −4
2. 4 or −8
3. 2 or −6
4. −1.5 or 1.5
5. 0 or −
4
3
6. 2 or −2
7. 4
8. −5
9. 1
10. −2 or −3
11. −3 or −7 12. 2 or −1
13. 4 or −3
14. 2 or 7
15. −4
16. 2
17. −3
18. 3 or −3
19. −2 or −
2
3
20. −1.5
21.
1
8
or −
1
8
22. 4 or −7
23. −1 or 1.5 24.
1
2
or
1
3
25.
1
2
or −
4
5
26. 1
1
3
or −
1
7
27.
3
8
or −2
28.
2
5
or −3
29.
4
3
or −
1
2
30.
5
4
or −
3
2
31. x
2
− 4x + 3 = 0 32. x
2
+ 3x − 10 = 0
33. x 2 + 5x + 4 = 0 34. 4x 2 − 8x − 5 = 0
35. x 2 − 36 = 0
36. x 2 − 1.7x − 1.68 = 0
Exercise 55 (page 106)
1. −3.732 or −0.268
2. −3.137 or 0.637
3. 1.468 or −1.135
4. 1.290 or 0.310
5. 2.443 or 0.307
6. −2.851 or 0.351
Exercise 56 (page 107)
1. 0.637 or −3.137
2. 0.296 or −0.792
3. 2.781 or 0.719
4. 0.443 or −1.693
5. 3.608 or −1.108
6. 1.434 or 0.232
7. 0.851 or −2.351
8. 2.086 or −0.086
9. 1.481 or −1.081
10. 4.176 or −1.676
11. 4 or 2.167
12. 7.141 or −3.641
13. 4.562 or 0.438
Exercise 57 (page 109)
1. 1.191 s 2. 0.345 A or 0.905 A 3. 7.84 cm
4. 0.619 m or 19.38 m
5. 0.0133
6. 1.066 m
7. 86.78 cm
8. 1.835 m or 18.165 m
9. 7 m
10. 12 ohms, 28 ohms
Exercise 58 (page 110)
1. x = 1, y = 3 and x = −3, y = 7
2. x =
2
5
, y = −
1
5
and −1
2
3
, y = −4
1
3
3. x = 0, y = 4 and x = 3, y = 1
Chapter 15
Exercise 59 (page 112)
1. 4
2. 4
3. 3
4. −3 5.
1
3
6. 3
7. 2
8. −2
9. 1
1
2
10.
1
3
11. 2
12. 10 000 13. 100 000 14. 9 15.
1
32
16. 0.01 17.
1
16
18. e 3
Exercise 60 (page 115)
1. log 6
2. log 15
3. log 2
4. log 3
5. log 12 6. log 500
7. log 100 8. log 6
9. log 10 10. log 1 = 0 11. log 2
12. log 243 or log 3 5 or 5 log3
13. log 16 or log2 4 or 4 log2
14. log 64 or log2 6 or 6 log2
15. 0.5
16. 1.5
17. x = 2.5 18. t = 8
19. b = 2 20. x = 2
21. a = 6 22. x = 5
Exercise 61 (page 116)
1. 1.690 2. 3.170 3. 0.2696 4. 6.058 5. 2.251
6. 3.959 7. 2.542 8. −0.3272 9. 316.2
5. x = 2, y = 4, z = 5 6. x = 1, y = 6, z = 7
7. x = 5, y = 4, z = 2 8. x = −4, y = 3, z = 2
9. x = 1.5, y = 2.5, z = 4.5
10. i 1 = −5, i 2 = −4, i 3 = 2
11. F 1 = 2, F 2 = −3 F 3 = 4
Chapter 14
Exercise 54 (page 104)
1. 4 or −4
2. 4 or −8
3. 2 or −6
4. −1.5 or 1.5
5. 0 or −
4
3
6. 2 or −2
7. 4
8. −5
9. 1
10. −2 or −3
11. −3 or −7 12. 2 or −1
13. 4 or −3
14. 2 or 7
15. −4
16. 2
17. −3
18. 3 or −3
19. −2 or −
2
3
20. −1.5
21.
1
8
or −
1
8
22. 4 or −7
23. −1 or 1.5 24.
1
2
or
1
3
25.
1
2
or −
4
5
26. 1
1
3
or −
1
7
27.
3
8
or −2
28.
2
5
or −3
29.
4
3
or −
1
2
30.
5
4
or −
3
2
31. x
2
− 4x + 3 = 0 32. x
2
+ 3x − 10 = 0
33. x 2 + 5x + 4 = 0 34. 4x 2 − 8x − 5 = 0
35. x 2 − 36 = 0
36. x 2 − 1.7x − 1.68 = 0
Exercise 55 (page 106)
1. −3.732 or −0.268
2. −3.137 or 0.637
3. 1.468 or −1.135
4. 1.290 or 0.310
5. 2.443 or 0.307
6. −2.851 or 0.351
Exercise 56 (page 107)
1. 0.637 or −3.137
2. 0.296 or −0.792
3. 2.781 or 0.719
4. 0.443 or −1.693
5. 3.608 or −1.108
6. 1.434 or 0.232
7. 0.851 or −2.351
8. 2.086 or −0.086
9. 1.481 or −1.081
10. 4.176 or −1.676
11. 4 or 2.167
12. 7.141 or −3.641
13. 4.562 or 0.438
Exercise 57 (page 109)
1. 1.191 s 2. 0.345 A or 0.905 A 3. 7.84 cm
4. 0.619 m or 19.38 m
5. 0.0133
6. 1.066 m
7. 86.78 cm
8. 1.835 m or 18.165 m
9. 7 m
10. 12 ohms, 28 ohms
Exercise 58 (page 110)
1. x = 1, y = 3 and x = −3, y = 7
2. x =
2
5
, y = −
1
5
and −1
2
3
, y = −4
1
3
3. x = 0, y = 4 and x = 3, y = 1
Chapter 15
Exercise 59 (page 112)
1. 4
2. 4
3. 3
4. −3 5.
1
3
6. 3
7. 2
8. −2
9. 1
1
2
10.
1
3
11. 2
12. 10 000 13. 100 000 14. 9 15.
1
32
16. 0.01 17.
1
16
18. e 3
Exercise 60 (page 115)
1. log 6
2. log 15
3. log 2
4. log 3
5. log 12 6. log 500
7. log 100 8. log 6
9. log 10 10. log 1 = 0 11. log 2
12. log 243 or log 3 5 or 5 log3
13. log 16 or log2 4 or 4 log2
14. log 64 or log2 6 or 6 log2
15. 0.5
16. 1.5
17. x = 2.5 18. t = 8
19. b = 2 20. x = 2
21. a = 6 22. x = 5
Exercise 61 (page 116)
1. 1.690 2. 3.170 3. 0.2696 4. 6.058 5. 2.251
6. 3.959 7. 2.542 8. −0.3272 9. 316.2