Exercise: Logarithm

Questions for: Logarithm

The value of log2 16 is:
A:
1
8
B:
4
C:
8
D:
16
Answer: B

Let log2 16 = n.

Then, 2n = 16 = 24         n = 4.

log2 16 = 4.

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

log 2 x = 10         x = 210.

logx y = 100

y = x100

y = (210)100     [put value of x]

y = 21000.

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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: C

ax = by

log ax = log by

x log a = y log b

log a = y .
log b x

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If logx 9 = - 1 , then x is equal to:
16 2
A:
- 3
4
B:
3
4
C:
81
256
D:
256
81
Answer: D

logx 9 = - 1
16 2

x-1/2 = 9
16

1 = 9
x 16

x = 16
9

x = 16 2
9

x = 256
81

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

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.

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