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Aptitude - Logarithm

Exercise : Logarithm - General Questions
1.
Which of the following statements is not correct?
log10 10 = 1
log (2 + 3) = log (2 x 3)
log10 1 = 0
log (1 + 2 + 3) = log 1 + log 2 + log 3
Answer: Option
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.

2.
If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:
2.870
2.967
3.876
3.912
Answer: Option
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
3.
log 8 is equal to:
log 8
1
8
1
4
1
2
1
8
Answer: Option
Explanation:
log 8 = log (8)1/2 = log 8 = 1 .
log 8 log 8 log 8 2
4.
If log 27 = 1.431, then the value of log 9 is:
0.934
0.945
0.954
0.958
Answer: Option
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.

5.
If log a + log b = log (a + b), then:
b a
a + b = 1
a - b = 1
a = b
a2 - b2 = 1
Answer: Option
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.

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