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- Question
If logx ❨ 9 ❩ = - 1 , then x is equal to: 16 2
Options- A.
- 3 4 - B.
3 4 - C.
81 256 - D.
256 81 - Correct Answer
-
256 81
Explanationlogx ❨ 9 ❩ = - 1 16 2 ⟹ x-1/2 = 9 16 ⟹ 1 = 9 √x 16 ⟹ √x = 16 9 ⟹ x = ❨ 16 ❩ 2 9 ⟹ x = 256 81
Logarithm problems
Search Results
- 1.
log √8 is equal to: log 8
Options- A.
1 √8 - B.
1 4 - C.
1 2 - D.
1 8
Discuss
Correct Answer:1 2
Explanation:
log √8 = log (8)1/2 = ½log 8 = 1 . log 8 log 8 log 8 2 - 2. If logx y = 100 and log2 x = 10, then the value of y is:
Options- A. 210
- B. 2100
- C. 21000
- D. 210000 Discuss
Correct Answer: 21000
Explanation:
log 2 x = 10 ⟹ x = 210.∴ logx y = 100
⟹ y = x100
⟹ y = (210)100 [put value of x]
⟹ y = 21000.
- 3.
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
Correct Answer: - (1 + a)
Explanation:
log10 ❨ 1 ❩ 70 = log10 1 - log10 70 = - log10 (7 x 10) = - (log10 7 + log10 10) = - (a + 1). - 4. 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
Correct Answer: 3.876
Explanation:
log5 512 = log 512 log 5 = log 29 log (10/2) = 9 log 2 log 10 - log 2 = (9 x 0.3010) 1 - 0.3010 = 2.709 0.699 = 2709 699 = 3.876 - 5. If log 2 = 0.30103, the number of digits in 264 is:
Options- A. 18
- B. 19
- C. 20
- D. 21 Discuss
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.
- 6. 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
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.
- 7.
The value of ❨ 1 + 1 + 1 ❩ is: log3 60 log4 60 log5 60
Options- A. 0
- B. 1
- C. 5
- D. 60 Discuss
Correct Answer: 1
Explanation:
Given expression = log60 3 + log60 4 + log60 5 = log60 (3 x 4 x 5) = log60 60 = 1. - 8. 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
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 - 9. 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
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.
- 10. A 6% stock yields 8%. The market value of the stock is:
Options- A. Rs. 48
- B. Rs. 75
- C. Rs. 96
- D. Rs. 133.33 Discuss
Correct Answer: Rs. 75
Explanation:
For an income of Rs. 8, investment = Rs. 100.For an income of Rs. 6, investment = Rs. ❨ 100 x 6 ❩ = Rs. 75. 8 ∴ Market value of Rs. 100 stock = Rs. 75.
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