Questions

logarithm aptitude questions

1. Which of the following statements is not correct?
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

Answer: Option B

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:
A. 2.870 B. 2.967
C. 3.876 D. 3.912

Answer: Option C

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
A.
1
8
B.
1
4
C.
1
2
D.
1
8

Answer: Option C

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:
A. 0.934 B. 0.945
C. 0.954 D. 0.958

Answer: Option C

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. a + b = 1 B. a – b = 1
C. a = b D. a2 – b2 = 1

Answer: Option A

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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