# 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

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. 2.87 B. 2.967 C. 3.876 D. 3.912

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

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

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

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.