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- Question
log √8 is equal to: log 8
Options- A.
1 √8 - B.
1 4 - C.
1 2 - D.
1 8 - Correct Answer
-
1 2
Explanationlog √8 = log (8)1/2 = ½log 8 = 1 . log 8 log 8 log 8 2 - 1. If logx y = 100 and log2 x = 10, then the value of y is:
Options- A. 210
- B. 2100
- C. 21000
- D. 210000 Discuss
- 2.
If log10 7 = a, then log10 ❨ 1 ❩ is equal to: 70
Options- A. - (1 + a)
- B. (1 + a)-1
- C.
a 10 - D.
1 10a
Discuss
- 3. If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:
Options- A. 2.870
- B. 2.967
- C. 3.876
- D. 3.912 Discuss
- 4. If log 2 = 0.30103, the number of digits in 264 is:
Options- A. 18
- B. 19
- C. 20
- D. 21 Discuss
- 5. Which of the following statements is not correct?
Options- A. log10 10 = 1
- B. log (2 + 3) = log (2 x 3)
- C. log10 1 = 0
- D. log (1 + 2 + 3) = log 1 + log 2 + log 3 Discuss
- 6.
If logx ❨ 9 ❩ = - 1 , then x is equal to: 16 2
Options- A.
- 3 4 - B.
3 4 - C.
81 256 - D.
256 81
Discuss
- 7. If log 27 = 1.431, then the value of log 9 is:
Options- A. 0.934
- B. 0.945
- C. 0.954
- D. 0.958 Discuss
- 8.
The value of ❨ 1 + 1 + 1 ❩ is: log3 60 log4 60 log5 60
Options- A. 0
- B. 1
- C. 5
- D. 60 Discuss
- 9. A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio:
Options- A. 3 : 4
- B. 3 : 5
- C. 4 : 5
- D. 16 : 15 Discuss
- 10. By investing Rs. 1620 in 8% stock, Michael earns Rs. 135. The stock is then quoted at:
Options- A. Rs. 80
- B. Rs. 96
- C. Rs. 106
- D. Rs. 108 Discuss
Logarithm problems
Search Results
Correct Answer: 21000
Explanation:
log 2 x = 10 ⟹ x = 210.
∴ logx y = 100
⟹ y = x100
⟹ y = (210)100 [put value of x]
⟹ y = 21000.
Correct Answer: - (1 + a)
Explanation:
|
= log10 1 - log10 70 | |||||
| = - log10 (7 x 10) | ||||||
| = - (log10 7 + log10 10) | ||||||
| = - (a + 1). |
Correct Answer: 3.876
Explanation:
| log5 512 |
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| = 3.876 |
Correct Answer: 20
Explanation:
| log (264) | = 64 x log 2 |
| = (64 x 0.30103) | |
| = 19.26592 |
Its characteristic is 19.
Hence, then number of digits in 264 is 20.
Correct Answer: log (2 + 3) = log (2 x 3)
Explanation:
(a) Since loga a = 1, so log10 10 = 1.
(b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3
∴ log (2 + 3) ≠ log (2 x 3)
(c) Since loga 1 = 0, so log10 1 = 0.
(d) log (1 + 2 + 3) = log 6 = log (1 x 2 x 3) = log 1 + log 2 + log 3.
So, (b) is incorrect.
Correct Answer:
| 256 |
| 81 |
Explanation:
| logx | ❨ | 9 | ❩ | = - | 1 |
| 16 | 2 |
| ⟹ x-1/2 | = | 9 |
| 16 |
| ⟹ | 1 | = | 9 |
| √x | 16 |
| ⟹ √x = | 16 |
| 9 |
| ⟹ x = | ❨ | 16 | ❩ | 2 |
| 9 |
| ⟹ x = | 256 |
| 81 |
Correct Answer: 0.954
Explanation:
log 27 = 1.431
⟹ log (33 ) = 1.431
⟹ 3 log 3 = 1.431
⟹ log 3 = 0.477
∴ log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954.
Correct Answer: 1
Explanation:
| Given expression | = log60 3 + log60 4 + log60 5 |
| = log60 (3 x 4 x 5) | |
| = log60 60 | |
| = 1. |
Correct Answer: 16 : 15
Explanation:
| For an income of Re. 1 in 9% stock at 96, investment = Rs. | ❨ | 96 | ❩ | = Rs. | 32 |
| 9 | 3 |
| For an income Re. 1 in 12% stock at 120, investment = Rs. | ❨ | 120 | ❩ | = Rs. 10. |
| 12 |
| ∴ Ratio of investments = | 32 | : 10 = 32 : 30 = 16 : 15. |
| 3 |
Correct Answer: Rs. 96
Explanation:
To earn Rs. 135, investment = Rs. 1620.
| To earn Rs. 8, investment = Rs. | ❨ | 1620 | x 8 | ❩ | = Rs. 96. |
| 135 |
∴ Market value of Rs. 100 stock = Rs. 96.
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