Logarithm problems
- 1. If log 3 = 0.477 and (1000) x = 3, then x equals to?
Options- A. 0.159
- B. 10
- C. 0.0477
- D. 0.0159 Discuss
Correct Answer: 0.159
Explanation:
? (1000)x = 3
? xlog 103 = log 3
? 3x = log 3
? x = log 3 / 3 = 0.477 / 3 = 0.159
- 2. If 5 5-x = 2 x-5, find the value of x .?
Options- A. 5
- B. 0
- C. 1
- D. Can't be determined Discuss
Correct Answer: 5
Explanation:
? 55-x = 2x-5
? 55-x = 2-(5-x)
? (5-x)log 5 = -(5-x)log 2
? (5-x)log 5 + (5-x)log 2 = 0
? (5-x){log 5 + log 2 } = 0
? (5-x){log10/2 + log 2 } = 0
? (5-x){log10 - log 2 + log 2} = 0
? 5-x = 0
? x = 5
- 3. If log 8 x + log 4 x + log 2x =11, then the value of x is?
Options- A. 2
- B. 4
- C. 8
- D. 64 Discuss
Correct Answer: 64
Explanation:
? log23 x1 +log22 x1 + log2x = 11
? 1/3log2x + 1/2log2x + log2x = 11
? (1/3 + 1/2 +1)log2x = 11
? 11/6log2x = 11
? log2x = 11 x 6 / 11 =6
? x = 26 = 64
- 4. If 10 0.3010 = 2, then find the value of log 0.125 125.?
Options- A. 699 / 301
- B. - 699 / 301
- C. - 1
- D. - 2 Discuss
Correct Answer: - 699 / 301
Explanation:
Exp. = log0.125125 = log2-3 53 = - 3/3log25 = -log25
? 100.3010 = 2
? log102 = 0.3010
? log105 = log1010/2 = log1010-log102
= 1-0.3010 = 0.6990
? -log25 = - log105 / log102
= - 0.6990 / 0.3010 = - 699/301
- 5. Find the value of log 0.125 64?
Options- A. - 2
- B. 2
- C. 0
- D. Can't be determined Discuss
Correct Answer: Can't be determined
Explanation:
Exp. = log0.12564 = log2-3 26
={6 / (-3)} log22
= -2
- 6. Find the value of log 322 8 + log 2433 7 - log 361296?
Options- A. 3
- B. 2
- C. 1
- D. 0 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 1
Explanation:
Exp. =log3228 + log24337 - log361296
= log25 28 + log35 37 - log36 362
= (8/5)log22 + (7/5)log33 - 2log3636
= 8/5 + 7/5 - 2 = 1
- 7. Find the value of log 49 16807 - log 9 27?
Options- A. 0
- B. 1
- C. 3 / 2
- D. - 1 Discuss
Correct Answer: 1
Explanation:
Exp. = log4916807 - log927
= log72 75 - log32 33
=(5/2)log77 - (3/2)log33
=5/2 - 3/2
= 1
- 8. Find the value of log 9 81 - log 4 32?
Options- A. 1 / 2
- B. - 3 / 2
- C. - 1 / 2
- D. 2 Discuss
Correct Answer: - 1 / 2
Explanation:
log9 81 - log4 32 = log32 34 - log22 25
= 4/2 - 5/2 = -1/2
- 9. log 1010 + log 10100 + log 101000 + log 1010000 + log 10100000 is equal to?
Options- A. 15
- B. log 11111
- C. log101111
- D. 14 log10 100 Discuss
Correct Answer: 15
Explanation:
Given Exp. = log1010 + log10100 + log101000 + log1010000 + log10100000
= 1 + 2 + 3 + 4 + 5
= 15
- 10. log 10x + log 10y = z, then x is equal to?
Options- A. z / y
- B. 10 / z
- C. 102 / x
- D. None of these Discuss
Correct Answer: None of these
Explanation:
log10xy = z
? xy = 10z
? x = 10z/y
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