# Common Logarithms Questions and Answers - Form 2 Topical Mathematics

## Questions

1. Use mathematical table to evaluate.

2. Given that y = Bxn. Make n the subject of the formula and simplify your answer
3. Without using mathematical tables or calculators evaluate: 6log264 + 10log3(243)
4. Find the value of x that satisfies the equation log (2x – 11) – log 2 =log 3 – log x
5. Use logarithms to evaluate to 3 significant figures

6. Use logarithm tables in all your steps to evaluate:

7. Make L the subject in :

8. Using logarithm tables solve.

9. Solve the simultaneous equation:-
Log (x-1) + 2log y = 2log3
log x + log y = log 6
10. Without using logarithms tables or calculator evaluate:-
4/5log1032 + log1050-3log10
11. Use logarithms to evaluate:-

and express the answer in standard form
12. Solve for x given that :- log (3x + 8) – 3log2 = log (x-4)
13. 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:
14. Use logarithms to evaluate correct to 4 s.f

15. Without using logarithm tables evaluate:

16. Without using a calculator/mathematical tables, solve: Log8 (x + 5) – log8(x -3) = Log84
17. Use tables to calculate;(6.572 + 6.57) ÷ (7.922 x 30.08)(Give your answer to 4 decimal places)
18. If log2 = 0.30103, and log3 = 0.47712, calculate without using tables or calculators the value of log120
19. Solve for x in the following equation; Log2(3x -4) = 1/3log28x6 – log24
20. By showing all the steps, use logarithms to evaluate:

21. Solve the logarithimic equation: log10(6x – 2) – 1 = log10 (- 3)
22. 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:-

23. Evaluate using logarithms

1.
2. Log y = log B + n log x
n log x = log y – log B
n = Log (y/B)/Log x
3. = 6 log24 + 10 log33
= 12 log22 + 10 log33
= 12 + 10
4. Log (2x - 11)/2 = log 3/x
(2x – 11) = 3/x
2x2 _ 11x -6 = 0
(2x + 1 ) (x – 6) = 0
x = - ½ or 6
x = 6
5.
6.
7. H3 = 3d(L - d)/10L
3dL - 10H3L= 3d2
L(3d -10H3)3d2
L = 3d2/3d - 10H3
8.
9. 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)/y = 9
6y – y2 = 9
y2– 6y + 9 = 0
(y-3)2 = 0
y = 3
x = 2
10. 4/5 log1025 + log1025x2 – log 10
4log 2 = log1025x2 – 3log2
2log10 + 2log5
Log 10 x 100
11.
12. Log 3x + 8 – log 8 = log (x-4)
Log (3x + 8)/8 = log (x-4)
3x + 8 = x -4
3x + 8 = 8x – 32
5x = 40
13.
14.
15. From square roots 12.25 = 3.5
3.264 x 1.215 x 3.5x√107
1.088 x 0.4725 x 107
3264 x 1215 x35
1088 x 4725
√27 = 3
16. Log8(x + 5) – log8(x -3) = Log84
Log8(x + 5)/x – 3 = log84
x + 5 = 4
x – 3
4x – 12 = x + 5
3x = 17
x = 17/3 = 52/3
Or log8x+5/x-3 = 2/3
8 2/3 = x + 5/x – 3
23(2/3) = x + 5/x -3
22 = x +5/x - 34 = x + 5/x - 3
4x -12 = x + 5 3x = 17
x = 17/3 = 52/3
17.
18. Log 120 = log 4 + log 3 + log 10
= log22 + log3 + log 10
= 2log2 + log3 + log 10
= 2(0.30103) + 0.47712 + 1
= 2.07918
19. Log2 (3x – 4) = 1/3 lo28x6 – log24
Log2 (3x – 4) = log2(23x6) - log24
Log2 (3x – 4) = log22x2 – 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
20.
21. Det 2 - -3 = 5
Area of AIBICI = 5 x 15
= 75 cm2
22. Log10(6x-2) – log10 = log10(x-3)
Log (6x -2)/10 = log (x-3)
6x - 2/10 = x -3
6x – 2 = 10x -30
x = 7
23. No.                    Log
0.075262           2.8766 x 2 = 3.7532
6.652                 0.8230 = 0.8230
4.9302/3 = 6 + 2.9302/3
= 2.9767
Antilog = 9.4776 x 10-2
= 0.094776(accept 0.09478)

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