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the Test
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WORKINGS

2. Question 1
Evaluate 𝑙𝑜𝑔5 (3/5) + 3 𝑙𝑜𝑔5 (5/2) -𝑙𝑜𝑔5(81/8)
A. 3- 3𝑙𝑜𝑔56
B. 3- 𝑙𝑜𝑔532
C. 2- 𝑙𝑜𝑔54
D. 2- 3𝑙𝑜𝑔53
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3. Question 2
Solve 𝑙𝑜𝑔512.5 +𝑙𝑜𝑔52
A. 3
B. 2
C. 4
D. 5
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4. Question 3
Simplify 𝑙𝑜𝑔327 x 2𝑙𝑜𝑔39 - 𝑙𝑜𝑔354
A. 4- 𝑙𝑜𝑔32
B. 3 - 𝑙𝑜𝑔33
C. 5-𝑙𝑜𝑔38
D. 1-𝑙𝑜𝑔321

5. Question 4
Solve log (20/9) + 2log (6/3) – log (4/125)
A. 2
B. 3
C. 4
D. 5

6. Question 5
If 𝑙𝑜𝑔3(x2 + 7x + 21) = 2, find x
A. -4, -2
B. -3, -4
C. -5, -4
D. -4, 5

7. Question 6
Evaluate log 7 + 2log 2 – log 280
A. 1
B. -1
C. 3
D. 2

8. Question 7
Solve 𝑙𝑜𝑔8 (x2 – 8x +18) = 1/3
A. 5
B. 2
C. 4 twice
D. 5 twice

9. Evaluate 𝑙𝑜𝑔5 0.04
A. 6-2
B. 4-2
C. 2
D. -2

10. Question 9
Solve 𝑙𝑜𝑔4(x2 +6x +11) = ½
A. -4 twice
B. -3 twice
C. -7 twice
D. -3

11. 10. Evaluate 𝑙𝑜𝑔927
A. 2
B. 3
C. 1
D. 1½

12. 11. Given that 𝑙𝑜𝑔4x = -3 , find x
A.
1
81
B.
1
64
C.
8
70
D.
1
54

13. 12. Solve the equation: 𝑙𝑜𝑔3(4x +1) - 𝑙𝑜𝑔3 (3x -5) =2
A. 3
B. 5
C. 2
D. 7

14. 13. Evaluate 𝑙𝑜𝑔232
A. 5
B. 6
C. 7
D. 4

15. 14. If 5 𝑥
= 125, find the value of x
A. 12
B. 4
C. 3
D. -3

16. 15. Simplify 3𝑦5
x 7𝑦2
A. 21𝑦6
B. 21𝑦5
C. 24𝑦7
D. 21𝑦7

17. 16. Solve the equation: 2𝑎−1/2
= −14
A.
4
49
B.
1
49
C.
3
49
D. 1

18. 17. Simplify 53𝑥+2
𝑋 54𝑥−1
A. 2
B. 7x +1
C. 57𝑥+1
D. 56𝑥+2

19. 18. If 𝑥3
= 27, find the value of x
A. 4
B. 3
C. -3
D. 9

20. 19. Solve the equation: 22𝑥+1
- 9(2 𝑥
) + 4 =0
A. -1, -2
B. -1, 2
C. 2, 2
D. -2, 1

21. 20. Simplify( 18/32)-3/2
A.
50
61
B.
71
83
C.
61
73
D.
64
27

22. 21. Simplify 12𝑚3
÷ 4𝑚3
B. 3𝑚2
A. 6𝑚2
C. 9𝑚2
D. 3𝑚4

23. 22. If (21−𝑦
𝑋2 𝑦−1
) ÷ 2 𝑦+2
= 82−3𝑦
, find 𝑦 𝑥−8
A. 4
B. 3
C. 1
D. 0

24. 23. Solve for x in the equation; 27(3𝑥+2)
= 9(5𝑥−4)
A. 14
B. 16
C. 20
D. 7

25. 24. Given that 𝑙𝑜𝑔102= 0.3010 and 𝑙𝑜𝑔103 = 0.4771,
Evaluate 𝑙𝑜𝑔109
A. 0.6543
B. 0.9876
C. 0.9542
D. 0.8754

26. 25. Given that 𝑙𝑜𝑔102= 0.3010 and 𝑙𝑜𝑔103 = 0.4771,
Evaluate 𝑙𝑜𝑔1012
A. 1.0791
B. 1.2346
C. 1.4567
D. 1.2345

27. 26. Given that 𝑙𝑜𝑔102= 0.3010 and 𝑙𝑜𝑔103 = 0.4771,
Solve 𝑙𝑜𝑔1015
A. 1.234
B. 1.1761
C. 1.1278
D. 1.2789

28. 27. Given that log 2 = 0.30103 and log 3 = 0.47712,
calculate without using any table
Log 5
A. 0.69897
B. 0.67894
C. 0.6453
D. 0.64231

29. 28. Given that log 2 = 0.30103 and log 3 = 0.47712,
calculate without using any table
Log 6
A. 0.76543
B. 0.77815
C. 0.76451
D. 0.37658

30. 29. Given that log 2 = 0.30103 and log 3 =
0.47712, calculate without using any table
Log 0.9
A. -0.7654
B. 0.04576
C. -0.86758
D. -0.34526

31. 30. Simplify log 8 + log 5
A. Log 40
B. Log 20
C. Log 10
D. Log 30

32. 31. Solve 2 – log 4
A. Log 30
B. Log 40
C. Log 25
D. Log 35

33. Simplify log 9 ÷ log 3
A. 4
B. 2
C. 3
D. 7

34. 33. Simplify 2/5 log 32
A. 3 log 2
B. 4 log 3
C. 2 log 2
D. 3 log 5

35. 34. Evaluate 𝑙𝑜𝑔3 6.84 to 2 decimal places
A. 1.67
B. 1.75
C. 1.69
D. 1.86

36. 35. Find the value of K given that log K – log (K-2) = log 5
A. 1½
B. 23/5
C. 2½
D. 12/5

37. 36. Find the value of x given that 𝑙𝑜𝑔10 x (x+3) =1
A. -2 or -3
B. -5 or 2
C. -4 or -5
D. -2 or -7

38. 37. The value of log 100 is
A. 3
B. 4
C. 2
D. 1

39. 38. Simplify (53)2
A. 15625
B. 15789
C. 19354
D. 12543

40. 39. Simplify {(3t)-5}k
A. 1/6
4kt
B. 1/3
2kt
C. 1/3
5kt
D. 1/3
6kt

41. 40. The value of 𝑙𝑜𝑔10 (1/10) is
A. -2
B. 3
C. 1
D. -1

63. Very Good
Correct
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64. NO
IS WRONG
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