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Common Logarithms Questions
1. The product of a and is 31.59. Given that logarithm of a is 2.6182. Find using logarithm the value of b. to 4 significant figures. (4mks)
2. Evaluate without using mathematical tables or calculators,
2 log10 5 – ½ log10 64 + 2 log10 40. (3mks)
3. Use logarithm table to evaluate. (4 marks)
3 (0.0246)2 x 142
0.002 x 1.14
4. Without using log tables or a calculator; solve (4mks)
5. Solve for x given
1 x
.642 = 256 (3 marks)
8
6. Use logarithms to evaluate (4mks)
7. Use logarithms to evaluate (4 marks)
8. Use mathematical table to evaluate.
2849 x 0.00574
36.89 ÷ 0.023
9. Given that y = Bxn. Make n the subject of the formula and simplify your answer
10. Without using mathematical tables or calculators evaluate: 6log2 64 + 10log3 (243)
11. Find the value of x that satisfies the equation log (2x – 11) – log 2 =log 3 – log x
12. Use logarithms to evaluate to 3 significant figures
(0.5241)2 x 83.59
3 0.3563
13. Use logarithm tables in all your steps to evaluate:
leaving your answer to four decimal places
14. Make L the subject in :
H =
15. Using logarithm tables solve.
6.195 x 11.82
83.52
16. Solve the simultaneous equation:-
Log (x-1) + 2log y = 2log3
log x + log y = log 6
17. Without using logarithms tables or calculator evaluate:-
4 log1032 + log1050-3log10 2
5
18. Use logarithms to evaluate:-
6.598
(0.9895)2 x 0.004974 0.75 and express the answer in standard form
19. Solve for x given that :- log (3x + 8) – 3log2 = log (x-4)
20. In this question, show all the steps in your calculations, giving your answer at each stage.
Use logarithms correct to 4 decimal places to evaluate:
36.72 x (0.46)2
185.4
21. Use logarithms to evaluate correct to 4 s.f
sin 44.5
tan 14.90 x cos 82
22. Without using logarithm tables evaluate:
3.264 x 1.215 x 12.25
1.088 x 0.4725
23. Without using a calculator/mathematical tables, solve:
Log8 (x + 5) – log8(x -3) = Log8 4
24. Use tables to calculate (6.572 + 6.57) ÷ (7.922 x 30.08)(Give your answer to 4 decimal places)
25. If log₂ = 0.30103, and log₃ = 0.47712, calculate without using tables or calculators the
value of log120
26. Solve for x in the following equation; Log2(3x -4) = 1 log28x6 – log24 3
27. By showing all the steps, use logarithms to evaluate: 5.627 x (0.234)3
(8.237) ½
28. Solve the logarithimic equation: log10 (6x – 2) – 1 = log10 (x-3)
29. In this question, show all the steps in your calculations, giving your answers at each stage.
Use logarithms, correct to 4 d.p to evaluate:-
(0.07526)2
1.789 + 4.863
30. Evaluate using logarithms
Common logarithms Answers
1. | Log 31.59 1.4996 Log a 2.6182 Log b1/3 3 Log b 4.6442 b = 0.0004407 b = 0.0004 |
M1
M1 A1 B1 |
Subt b logs
Multip by 3 | |||
04 | ||||||
2. | Log1025 – log104 + log101600 | M1
M1
A1 | ||||
03 | ||||||
3 |
|
1M
1M
1M
A1 |
Correct logs addition
Correct logs addition
Correct logs substractions
Correct answer | |||
4 | ||||||
4 | -2 |
M1
M1
M1 A1 4 |
5. 1 x
. 26
2 = 24 2 M1 for writing in
23 index form
2-3x.212 = 28
12 – 3x = 8 M1
x = 4/3
= 1 1/3
3
6. | No. std form log 0.68452 6.845×10-1 1.6708 1.6708 0.08416 8.416×10-2 3 1.6417 1.6417 + 1.3125 0.005937 5.937×10-3 –3.7736 3.459×10-1 0.3459 |
M1
M1 M1 A1 | |||||||
04 | |||||||||
7 |
|
M1
M1
M1
A1
|
All logs
+ – x of logs
| ||||||
4 marks |
8. No. Log
2849 3.4547
+
0.00574 3. 7589
1.2136
36.891.1 1. 5669
0.023 2.3617
3.2052
2. 0084 x ¼
3.178 x 10-1 1. 5021
0.3178
9. Log y = log B + n log x
n log x = log y – log B
n = Log (y/B)
Log x
10. = 6 log2 4 + 10 log33
= 12 log22 + 10 log33
= 12 + 10
11. Log 2x – 11 = log 3
2 x
(2x – 11) = 3/x
2x2 _ 11x -6 = 0
(2x + 1 ) (x – 6) = 0
x = – ½ or 6
x = 6
12.
No. | Log |
0.5241 (0.5241)2
83.59
0.3563 3√0.3563
3.239×101 = 32.4 | T.7194 T.7194×2 T.4388 + 1.9222 1.3610 T.5518 (3+2.5518) 3 T.8506 0.3610 – 1.8506 1.5104 |
13. No. Log
38.32 1.5834
12.964 1.1127
2.6961
86.37 1.9364
6.285 0.7783
2.7347
1.9587
-3 + 2.9587 = 1.9866
3 = 0.9695
14. H3 = 3d(L-d)
10L
3dL -10H3L= 3d2
L(3d -10H3) 3d2
L = 3d2
3d -10H3
15. No. Log
6.195 0.7920
11.82 1.0726
1.8646
83.52 1.9218
1.9428 x ¼
4. + 3.9428
4
0.9676 1.9857
16. Log y2 (x-1) = log 9 y2 (x-1) = 9 ….(1)
log (xy) log 6 xy = 6 ….2
from (2) x = 6/y
substitute in (1) y(6 -1) = 9
y
6y – y2 = 9
y2 – 6y + 9 = 0
(y-3)2 = 0
y = 3
x = 2
5
17. 4/5 log1025 + log10 25×2 – log 10
4 log 2 = log 10 25×2 – 3log 2
2 log 10 + 2 log 5
Log 10 x 100
18.
| LOG |
0.9895 (0.9895)2
0.004974
6.598
3.579 X102 OR 357.9 |
1.9954 x 2 1.9908
3.68764
1.4219 x 3 2.2657 0.8195 – 2.2657 2.5538
|
19. Log 3x + 8 – log 8 = log (x-4)
Log (3x + 8) = log (x-4)
8
3x + 8 = x -4
3x + 8 = 8x – 32
5x = 40
20.
No. | Log |
36.72 0.462
185.4
Or 0.3474 | 1.5649 2(T.6628) T.3256 0.8905
2.9223 x 1 = 3 + 1.6223 3 3 3 1.5408 |
21. No Log
Sin 44.5 1.8457
Tan 14.9 1.4250 2.5686 –
Cos 82 1.1486 +
1.2772
2
10 x 4.351 __________ 0.6386
22. From square roots 12.25 = 3.5
3.264 x 1.215 x 3.5 x 107
1.088 x 0.4725 x 107
3264 x 1215 x35
1088 x 4725
27 = 3
23. Log8 (x + 5) – log8(x -3) = Log8 4
Log8 (x + 5) = log8 4
x – 3
x + 5 = 4
x – 3
4x – 12 = x + 5
3x = 17
x = 17 = 52/3
Or log 8 x +5 = 2
x – 3 3
8 2/3 = x + 5
x – 3
23( 2/3) = x + 5
x -3
22 = x +5
4 = x + 5
x -3 x – 3
4x -12 = x + 5 3x = 17
x = 17 = 52/3
3
24.
No 6.572
4.317 X 101 43.17 + 6.57
49.74 (7.92)2
30.08 2.636 X 10-2 | Log 0.8176 2x 1.6352
1.6967 0.8987 X2
1.7974 1.4783 + 3.2757 2.4210 = 0.02636 = 0.0264 (4 d.p) |
No 6.572
4.317 X 101 43.17 + 6.57
49.74 (7.92)2
30.08 2.636 X 10-2 | Log 0.8176 2x 1.6352
1.6967 0.8987 X2
1.7974 1.4783 + 3.2757 2.4210 = 0.02636 = 0.0264 (4 d.p) |
25. Log 120 = log 4 + log 3 + log 10
= log22 + log3 + log 10
= 2log2 + log3 + log 10
= 2(0.30103) + 0.47712 + 1
= 2.07918
26. Log2 (3x – 4) = 1/3 lo2 8x6 – log2 4
Log2 (3x – 4) = log2 (23x6) – log2 4
Log2 (3x – 4) = log2 2x2 – log2 4
Log2 (3x – 4) – log2
2x2
4
= 3x – 4 = 2x2
4
2x2 – 12x + 16 = 0
x2 – 6x + 8 = 0
x – 2x – 4x + 8 = 0
(x – 2) (x- 4) = 0
x = 2 or x = 4
27.
No 5.627 (0.234)3
8.237
2.399 x 10-3 | Log 0.7503 T. 3692
2.8579
0.4779 0.9158 2 3.3800
= 0.002399 |
28. Det 2 – -3 = 5
Area of AIBICI = 5 x 15
= 75 cm2
29. Log10(6x-2) – log10 = log10(x-3)
Log (6x -2) = log (x-3)
10
6x -2 = x -3
10
6x – 2 = 10x -30
x = 7
30. No. Log
0.075262 2.8766 x 2 = 3.7532
6.652 0.8230 = 0.8230
4.9302
4.9302 = 6 + 2.9302
3 3
= 2.9767
Antilog = 9.4776 x 10-2
= 0.094776(accept 0.09478)
No. Log
- 0.6317
0.0094782 3.9767 X 2 +
5. 9534
4.5851 –
Log 9.814 1.9964
4. 5887
5
2.0785 X 10-1 1.3177
= 0.20785