Logarithm problems
- 1.
If log a + log b = log (a + b), then: b a
Options- A. a + b = 1
- B. a - b = 1
- C. a = b
- D. a2 - b2 = 1 Discuss
Correct Answer: a + b = 1
Explanation:
| log | a | + log | b | = log (a + b) |
| b | a |
| ⟹ log (a + b) = log | ❨ | a | x | b | ❩ | = log 1. |
| b | a |
So, a + b = 1.
- 2. If ax = by, then:
Options- A.
log a = x b y - B.
log a = x log b y - C.
log a = y log b x - D. None of these Discuss
Correct Answer:
| log a | = | y |
| log b | x |
Explanation:
ax = by
⟹ log ax = log by
⟹ x log a = y log b
| ⟹ | log a | = | y | . |
| log b | x |
- 3. If log10 2 = 0.3010, then log2 10 is equal to:
Options- A.
699 301 - B.
1000 301 - C. 0.3010
- D. 0.6990 Discuss
Correct Answer:
| 1000 |
| 301 |
Explanation:
| log2 10 = | 1 | = | 1 | = | 10000 | = | 1000 | . |
| log10 2 | 0.3010 | 3010 | 301 |
- 4. If log10 2 = 0.3010, the value of log10 80 is:
Options- A. 1.6020
- B. 1.9030
- C. 3.9030
- D. None of these Discuss
Correct Answer: 1.9030
Explanation:
| log10 80 | = log10 (8 x 10) |
| = log10 8 + log10 10 | |
| = log10 (23 ) + 1 | |
| = 3 log10 2 + 1 | |
| = (3 x 0.3010) + 1 | |
| = 1.9030. |
- 5. The value of log2 16 is:
Options- A.
1 8 - B. 4
- C. 8
- D. 16 Discuss
Correct Answer: 4
Explanation:
Let log2 16 = n.
Then, 2n = 16 = 24 ⟹ n = 4.
∴ log2 16 = 4.
- 6. If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:
Options- A. 1
- B. 3
- C. 5
- D. 10 Also asked in: Bank Exams, Bank PO
Correct Answer: 3
Explanation:
log10 5 + log10 (5x + 1) = log10 (x + 5) + 1
⟹ log10 5 + log10 (5x + 1) = log10 (x + 5) + log10 10
⟹ log10 [5 (5x + 1)] = log10 [10(x + 5)]
⟹ 5(5x + 1) = 10(x + 5)
⟹ 5x + 1 = 2x + 10
⟹ 3x = 9
⟹ x = 3.
- 7. 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
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.
- 8. 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.
- 9. 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 |
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| = 3.876 |
- 10.
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 - log10 70 | |||||
| = - log10 (7 x 10) | ||||||
| = - (log10 7 + log10 10) | ||||||
| = - (a + 1). |
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