logarithm aptitude questions

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11. If log 2 = 0.30103, the number of digits in 264 is:
A. 18 B. 19
C. 20 D. 21

Answer: Option C

Explanation:

 

 

log (264) = 64 x log 2
= (64 x 0.30103)
= 19.26592

Its characteristic is 19.

Hence, then number of digits in 264 is 20.
12.
If logx 9 = – 1 , then x is equal to:
16 2
A.
– 3
4
B.
3
4
C.
81
256
D.
256
81

Answer: Option D

Explanation:

 

 

logx 9 = – 1
16 2

 

x-1/2 = 9
16

 

1 = 9
x 16

 

x = 16
9

 

x = 16 2
9

 

x = 256
81
13. If ax = by, then:
A.
log a = x
b y
B.
log a = x
log b y
C.
log a = y
log b x
D. None of these

Answer: Option C

Explanation:

 

ax = by

log ax = log by

x log a = y log b

 

log a = y .
log b x
14. If logx y = 100 and log2 x = 10, then the value of y is:
A. 210 B. 2100
C. 21000 D. 210000

Answer: Option C

Explanation:

 

log 2 x = 10         x = 210.

logx y = 100

y = x100

y = (210)100     [put value of x]

y = 21000.
15. The value of log2 16 is:
A.
1
8
B. 4
C. 8 D. 16

Answer: Option B

Explanation:

 

Let log2 16 = n.

Then, 2n = 16 = 24         n = 4.

log2 16 = 4.
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