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Logarithms Quiz 2
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Directions: Study the following questions carefully and choose the right answer:
Important for :
CDSE
1
If log
_{x}
8 = 0.6, then what is the value of of x is:
A
14
B
23
C
32
D
43
» Explain it
Correct Option:
C
log
_{x }
8 = 6/10 = 3/5
8 = x
^{3/5}
8
^{5/3}
= X
X = 2
^{5}
= 32.
Hence, option C is correct.
1
A
B
C
D
» Explain it
सही विकल्प :
C
C
2
What is the value of 36
^{log6 4}
?
A
12
B
16
C
18
D
24
» Explain it
Correct Option:
B
We know that : a
^{loga x}
= x.
∴
36
^{log6 4}
= (6
^{2}
)
^{log6 4}
= 6
^{2 log6 4}
= 6
^{log6 (42)}
= 6
^{log6 (16)}
= 16.
Hence, option B is correct.
2
A
B
C
D
» Explain it
सही विकल्प :
B
B
3
What is the value of log
_{3}
5 . log
_{25}
27 ?
A
1 / 2
B
2
C
3 / 2
D
3
» Explain it
Correct Option:
C
We know that log
_{a}
b = log b / log a.
∴ log
_{3}
5 . log
_{25}
27 = (log 5 / log3) × (log 27 / log 25)
= (log 5 / log 3) × (log 3
^{3}
/ log 5
^{2}
)
= (log 5 / log 3) × (3 log 3 / 2 log 5) = 3 / 2.
Hence, option C is correct.
3
A
B
C
D
» Explain it
सही विकल्प :
C
C
4
What is the value of log
_{9}
27 - log
_{27}
9 ?
A
1
B
1 / 2
C
5 / 6
D
2 / 3
» Explain it
Correct Option:
C
log
_{9}
27 = m ⇔ 9
^{m}
= 27 ⇔ 3
^{2}
^{m}
= 3
^{3}
⇔ 2m = 3 = 3/2.
⇒ m = 3/2
And, log
_{27}
9 = n ⇔ (27)
^{n}
= 9 ⇔ 3
^{3n}
= 3
^{2}
⇔ 3n = 2
⇒ n = 2 / 3
∴
log
_{9}
27 - log
_{27}
9 = 3/2 - 2/3 = (9-4)/6
⇒ 5/6.
Hence option C is correct.
4
A
B
C
D
» Explain it
सही विकल्प :
C
C
5
What is the value of [log
_{10}
(5 log
_{10}
100)]
^{2}
?
A
4
B
3
C
2
D
1
» Explain it
Correct Option:
D
[log
_{10}
(5 log
_{10}
100)]
^{2}
= [log
_{10}
(5 log
_{10}
10
^{2}
)]
^{2}
= [log
_{10}
(10 log
_{10}
10)]
^{2}
= [log
_{10}
10)]
^{2}
(
∵
log
_{10}
10 = 1)
= 1
^{2}
= 1.
Hence, option D is correct.
5
A
B
C
D
» Explain it
सही विकल्प :
D
D
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