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CBSE Questions for Class 11 Commerce Applied Mathematics Logarithm And Antilogarithm Quiz 3 - MCQExams.com
CBSE
Class 11 Commerce Applied Mathematics
Logarithm And Antilogarithm
Quiz 3
The value of
(
2
0
−
3
0
)
×
4
2
is---
Report Question
0%
16
0%
0
0%
−
16
0%
None of these
Explanation
(
2
0
−
3
0
)
×
4
2
=
(
1
−
1
)
×
4
2
=
0
×
16
=
0
If
log
x
=
n
then 2n is equal to
Report Question
0%
log
(
x
2
)
0%
(
log
x
)
2
0%
log
(
x
+
2
)
0%
log
2
x
Explanation
Given ,
log
x
=
n
We know that
log
x
2
=
2
log
x
⇒
2
n
=
2
log
x
=
log
x
2
Or
log
x
2
=
2
log
x
=
2
n
.
a
0
=
1
is true for all
a
except
Report Question
0%
−
1
0%
negative integers
0%
0
0%
1
Explanation
The correct answer is C
A.
(
−
1
)
0
=
1
B.
(
−
2
)
0
=
1
C.
0
0
is not defined.
D.
1
0
=
1
If
log
x
y
=
100
a
n
d
log
2
x
=
10
then the value of y is
Report Question
0%
2
1000
0%
2
100
0%
2
2000
0%
2
10000
Explanation
∵
l
o
g
2
x
=
10
∴
x
=
2
10
Also,
l
o
g
x
y
=
100
∴
y
=
x
100
Now, put the value of x then
y
=
2
1000
If
x
=
y
(
1
+
a
)
p
, then
p
is equal to
Report Question
0%
log
e
(
y
x
)
log
e
(
1
+
a
)
0%
log
{
y
x
(
1
+
a
)
}
0%
log
{
y
−
x
1
+
a
}
0%
log
y
log
{
x
(
1
+
a
)
}
Explanation
∵
x
=
y
(
1
+
a
)
p
∴
(
1
+
a
)
p
=
y
x
∴
p
log
e
(
1
+
a
)
=
log
e
y
x
∴
p
=
log
e
(
y
x
)
log
e
(
1
+
a
)
Which of the following expresses zero law of exponents?
Report Question
0%
0
x
=
0
0%
x
0
=
1
0%
x
1
=
x
0%
None of the above
Explanation
According to the zero law of exponents,
any non - zero number raised to the power of zero is equal to
1
.
∴
x
0
=
1
, where
x
≠
0
So, option
B
is correct.
4
×
4
10
is represented as:
Report Question
0%
4
40
0%
4
10
0%
4
11
0%
16
10
Explanation
4
×
4
10
=
4
1
+
10
=
4
11
So, option
C
is correct.
In simplified form,
(
(
3
)
0
+
(
5
)
0
)
0
is equal to:
Report Question
0%
2
0%
1
0%
0
0%
8
Explanation
(
3
0
+
5
0
)
0
=
(
1
+
1
)
0
=
(
2
)
0
=
1
So, option
B
is correct.
Find the value of
(
6
)
0
−
(
10
)
0
Report Question
0%
−
4
0%
2
0%
1
0%
0
Explanation
(
6
)
0
−
(
10
)
0
=
1
−
1
=
0
So, option
D
is correct.
The expression
(
(
2
)
0
+
(
3
)
0
+
(
5
)
0
)
0
is equal to _____
Report Question
0%
3
0%
1
0%
10
0%
0
Explanation
(
(
2
)
0
+
(
3
)
0
+
(
5
)
0
)
0
=
(
1
+
1
+
1
)
0
=
3
0
=
1
So, option
B
is the correct answer.
The value of
21
0
is _____.
Report Question
0%
0
0%
21
0%
1
0%
−
21
Explanation
21
0
=
1
∵
a
0
=
1
This is the law for zero exponent.
So, option
C
is correct.
Which of the following expresses product law of exponents?
Report Question
0%
(
a
m
)
n
=
a
m
n
0%
a
m
×
a
n
=
a
m
+
n
0%
a
m
÷
a
n
=
a
m
−
n
0%
a
m
÷
b
m
=
(
a
b
)
m
Explanation
The product law of exponents states that,
when multiplying two powers that have the same base,
we can add their exponents.
∴
a
m
×
a
n
=
a
m
+
n
So, option
B
is correct.
The value of
(
(
6
)
0
+
(
16
)
0
)
÷
(
(
7
)
0
+
(
17
)
0
)
is _____
Report Question
0%
2
0%
4
0%
1
0%
0
Explanation
(
(
6
)
0
+
(
16
)
0
)
÷
(
(
7
)
0
+
(
17
)
0
)
=
(
1
+
1
)
÷
(
1
+
1
)
=
2
÷
2
=
1
So, option
C
is correct.
The value of
(
100
)
0
is _____.
Report Question
0%
1
0%
0
0%
100
0%
1000
Explanation
According to the law of power of
0
,
(
100
)
0
=
1
.
So, option
A
is correct.
Evaluate:
(
(
10
)
0
+
(
12
)
0
)
×
(
18
)
0
Report Question
0%
1
0%
0
0%
2
0%
18
Explanation
(
(
10
)
0
+
(
12
)
0
)
×
(
18
)
0
=
(
1
+
1
)
×
1
=
(
2
)
×
1
=
2
So. option
C
is correct.
Given that
2
h
×
2
3
=
2
9
, find the value of h.
Report Question
0%
3
0%
6
0%
8
0%
12
Explanation
2
h
×
2
3
=
2
9
⇒
2
h
+
3
=
2
9
⇒
h
+
3
=
9
⇒
h
=
6
Find the correct expression, if
log
c
a
=
x
.
Report Question
0%
x
c
=
a
0%
a
x
=
c
0%
c
a
=
x
0%
c
x
=
a
0%
None of these
Explanation
Given,
log
c
a
=
x
Taking antilog, we get
c
x
=
a
.
Which one of the following is the value of
(
101
)
0
?
Report Question
0%
0
0%
101
0%
1010
0%
1
Explanation
101
0
=
1
So, option
D
is correct.
To simplify the following expression correctly, what must be done with the exponents?
5
a
×
5
b
×
5
c
Report Question
0%
Add the exponents.
0%
Multiply the exponents.
0%
Divide the exponents
0%
Subtract the exponents.
Explanation
Since the base is same, the exponents can be added (Product rule of exponents).
∴
5
a
×
5
b
×
5
c
=
5
(
a
+
b
+
c
)
Hence, option
A
is correct.
The value of
(
10
)
0
×
(
20
)
0
×
(
30
)
0
is:
Report Question
0%
1
0%
3
0%
60
0%
0
Explanation
(
10
)
0
×
(
20
)
0
×
(
30
)
0
=
1
×
1
×
1
=
1
So, option
A
is correct.
Which of the following is equal to
1
?
Report Question
0%
(
3
)
0
+
(
3
)
0
0%
(
3
)
0
−
(
3
)
0
0%
(
3
)
0
0%
(
3
3
)
0
+
(
3
0
)
3
Explanation
Step 1: Simplify the following expressions.
(
a
)
3
0
+
3
0
=
1
+
1
=
2
≠
1
(
b
)
3
0
−
3
0
=
1
−
1
=
0
≠
1
(
c
)
3
0
=
1
(
d
)
(
3
3
)
0
+
(
3
0
)
3
=
9
0
+
1
3
=
1
+
1
=
2
≠
1
Hence, Option C is correct.
Simplify and give reasons:
(
−
2
)
7
Report Question
0%
−
128
0%
128
0%
−
28
0%
None of these
Explanation
(
−
2
)
7
=
(
−
1
∗
2
)
7
=
(
−
1
)
7
(
2
)
7
∵
(
a
b
)
m
=
a
m
∗
b
m
=
−
1
∗
2
7
=
−
2
7
=
−
128
(
1000
)
9
÷
10
24
=
?
Report Question
0%
10000
0%
1000
0%
100
0%
10
0%
None of the above
Explanation
Given Exp.=
(
1000
)
9
10
24
=
(
10
3
)
9
10
24
=
10
27
10
24
=
10
(
27
−
24
)
=
10
3
=
1000
Simplify and give reasons:
(
−
3
)
−
4
Report Question
0%
1
81
0%
−
1
81
0%
3
81
0%
None of these
Explanation
(
−
3
)
−
4
=
(
−
1
∗
3
)
−
4
=
(
−
1
)
−
4
(
3
)
−
4
∵
(
a
b
)
m
=
a
m
∗
b
m
=
1
∗
3
−
4
=
3
−
4
∵
a
−
m
=
1
a
m
=
(
1
3
)
4
=
1
81
Simplify:
(
4
−
1
×
3
−
1
)
÷
6
−
1
Report Question
0%
1
2
0%
1
4
0%
2
2
0%
None of these
Explanation
we know,
a
m
∗
b
m
=
(
a
b
)
m
so,
4
−
1
∗
3
−
1
=
12
−
1
we know,
a
−
m
b
−
m
=
(
a
b
)
−
m
=
(
b
a
)
m
so,
12
−
1
6
−
1
=
2
−
1
=
1
2
Simplify the following:
(
−
2
)
7
×
(
−
2
)
3
×
(
−
2
)
4
Report Question
0%
(
−
2
)
14
0%
(
−
2
)
24
0%
(
−
2
)
54
0%
None of these
Explanation
we know,
a
m
∗
a
n
=
a
m
+
n
⟹
a
m
∗
a
n
∗
a
p
=
a
m
+
n
+
p
so,
(
−
2
)
7
×
(
−
2
)
3
×
(
−
2
)
4
=
(
−
2
)
7
+
3
+
4
=
(
−
2
)
14
Simplify and give reasons:
3
−
2
3
×
(
3
0
−
3
−
1
)
Report Question
0%
2
81
0%
1
81
0%
4
81
0%
None of these
The logarithmic form of
5
2
=
25
is
Report Question
0%
log
5
2
=
25
0%
log
2
5
=
25
0%
log
5
25
=
2
0%
log
25
5
=
2
Explanation
5
2
=
25
Taking log with base
5
both sides, we get
log
5
5
2
=
log
5
25
⇒
log
5
25
=
2
log
5
5
⇒
log
5
25
=
2
(
log
a
a
=
1
)
Hence, C is the correct option.
Exponential form of
log
4
8
=
x
is _____
Report Question
0%
x
8
=
4
0%
x
4
=
8
0%
4
x
=
8
0%
8
x
=
4
Explanation
We have,
log
4
8
=
x
If
log
b
a
=
x
then
a
=
b
x
So,
4
x
=
8
is the correct answer.
Option
C
is the correct answer.
The exponential form of
log
2
16
=
4
is
Report Question
0%
2
4
=
16
0%
4
2
=
16
0%
2
16
=
4
0%
4
16
=
2
Explanation
Since,
log
2
16
=
4
⟹
log
of
16
to the base
2
is
4
⇒
16
=
2
4
Hence, A is the correct option.
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