Exercise: Logarithm

Questions for: Logarithm

The value of 1 + 1 + 1 is:
log3 60 log4 60 log5 60
A:
0
B:
1
C:
5
D:
60
Answer: B
Given expression = log60 3 + log60 4 + log60 5
= log60 (3 x 4 x 5)
= log60 60
= 1.
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If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:
A:
1
B:
3
C:
5
D:
10
Answer: B

log10 5 + log10 (5x + 1) = log10 (x + 5) + 1

log10 5 + log10 (5x + 1) = log10 (x + 5) + log10 10

log10 [5 (5x + 1)] = log10 [10(x + 5)]

5(5x + 1) = 10(x + 5)

5x + 1 = 2x + 10

3x = 9

x = 3.

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If log10 2 = 0.3010, the value of log10 80 is:
A:
1.6020
B:
1.9030
C:
3.9030
D:
None of these
Answer: B
log10 80 = log10 (8 x 10)
= log10 8 + log10 10
= log10 (23 ) + 1
= 3 log10 2 + 1
= (3 x 0.3010) + 1
= 1.9030.
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If log10 2 = 0.3010, then log2 10 is equal to:
A:
699
301
B:
1000
301
C:
0.3010
D:
0.6990
Answer: B
log2 10 = 1 = 1 = 10000 = 1000 .
log10 2 0.3010 3010 301
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If log10 7 = a, then log10 1 is equal to:
70
A:
- (1 + a)
B:
(1 + a)-1
C:
a
10
D:
1
10a
Answer: A
log10 1
70
= log10 1 - log10 70
= - log10 (7 x 10)
= - (log10 7 + log10 10)
= - (a + 1).
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