Logarithm problems
- 1. The simplified form of log(75/16) -2 log(5/9) +log(32/343) is?
Options- A. log 2
- B. 2 log 2
- C. log 3
- D. log 5 Discuss
Correct Answer: log 2
Explanation:
Given Exp. = log75/16 - 2 log5/9 + log32/343
= log [(25 x 3) / (4 x 4)] - log (25/81) + log [(16 x 2) / (81 x 3)]
= log(25 x 3) - log ( 4 x 4 ) - log(25) + log81 + log(16 x 2) -log (81 x 3)
= log 25 + log 3 - log 16 - log 25 + log 81 + log 16 + log 2 - log 81 - log 3
= log 2
- 2. If log 2 = 0.3010 then log 5 equals to?
Options- A. 0.3010
- B. 0.6990
- C. 0.7525
- D. Given log 2, it is not possible to calculate log 5 Discuss
Correct Answer: 0.6990
Explanation:
log 5 = log 10 /2 = log 10 - log 2
= 1 - 0.3010 = 0.6990
- 3. If log 102 =0.3010 and log 107 = 0.8451, then the value of log 10 2.8 is?
Options- A. 0.4471
- B. 1.4471
- C. 2.4471
- D. 14.471 Discuss
Correct Answer: 0.4471
Explanation:
log102.8 = log10(28/10)
= log 28 - log 10
= log (7 x 4 ) - log 10
= log 7 + 2 log 2 - log 10
= 0.8451 + 2 x 0.3010 - 1
= 0.8451 + 0.6020 - 1
= 0.4471
- 4. If log 10 2 =0.301, then the value of log 10(50) is?
Options- A. 0.699
- B. 1.301
- C. 1.699
- D. 2.301 Discuss
Correct Answer: 1.699
Explanation:
log1050 = log10[(50 x 2) / 2]
= log 100 - log 2
= log10102 - log 2
= 2 - 0.301
= 1.699
- 5. Find the value of log (a 2 / bc) + log (b 2 / ac) + log (c 2 / ab)?
Options- A. 0
- B. 1
- C. abc
- D. ab2c2 Discuss
Correct Answer: 0
Explanation:
Given Exp. = log (a2 / bc) + log (b2 / ac) + log (c2 / ab)
= log [(a2 x b2 x c2) / (a2 x b2 x c2)]
=log 1
=0
- 6. Find the value of log 8 + log 1/8?
Options- A. 0
- B. 1
- C. 2
- D. log (64) Discuss
Correct Answer: 0
Explanation:
Given expression = log 8 + log (1/8)
= log 8 x (1/8)
= log 1
= 0
- 7. The equation log ax + log a (1+x)=0 can be written as?
Options- A. x2 + x - 1 = 0
- B. x2 + x + 1 = 0
- C. x2 + x - e = 0
- D. x2 + x + e = 0 Discuss
Correct Answer: x2 + x - 1 = 0
Explanation:
logax + loga(1+x) = 0
? logax (x+1) = loga1 (since log 1 = 0)
? x(x +1) = 1
? x2 + x - 1 = 0
- 8. Find the value of log x + log (1/x)?
Options- A. 0
- B. 1
- C. - 1
- D. 1/2 Discuss
Correct Answer: 0
Explanation:
Given expression = log x + log1/x
= log x + log 1 - log x
= log 1
= 0
- 9. If log 90 = 1.9542 then log 3 equals to?
Options- A. 0.9771
- B. 0.6514
- C. 0.4771
- D. 0.3181 Discuss
Correct Answer: 0.4771
Explanation:
Given log90 = 1.9542
? log(32 x 10) = 1.9542
? 2log 3 + log 10 = 1.9542
? log 3 = 0.9542 / 2 = 0.4771
- 10. If 2log 4x = 1 + log 4 (x-1), find the value of x.?
Options- A. 2
- B. 1
- C. 4
- D. 3 Discuss
Correct Answer: 2
Explanation:
? 2log4x = 1 + log4(x-1)
? log4x2 = log44 + log4(x-1)
? x2 = 4(x-1)
? x2 - 4x + 4 = 0
? (x-2)2 = 0
? x = 2
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