Logarithm

Logarithm

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Question 1
If log 27 = 1.431, then the value of log 9 is:
A
0.934
B
0.945
C
0.954
D
0.958
Question 1 Explanation: 
log 27 = 1.431 =>log (3(^3 ) = 1.431 ==>3 log 3 = 1.431 ==>log 3 = 0.477 ==>log 9 = log(3^2) = 2 log 3 = (2 x 0.477) = 0.954.
Question 2
If log(a/b)+log(b/a)= log (a + b), then:
A
a + b = 1
B
a - b = 1
C
a = b
D
a^2 - b^2 = 1
Question 2 Explanation: 
log (a + b) = log((a/b)*(b/a)) ==> log 1. So, a + b = 1.
Question 3
If log 2 = 0.30103, the number of digits in 2^64 is:
A
18
B
19
C
20
D
21
Question 3 Explanation: 
log (2^64)= 64 x log 2 = (64 x 0.30103) = 19.26592 Its characteristic is 19. Hence, then number of digits in 264 is 20.
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