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Byju's Answer
Standard XII
Mathematics
Standard Logarithm
State whether...
Question
State whether each of the following statements is true or false.
(i)
log
5
125
=
3
(ii)
log
1
2
8
=
3
(iii)
log
4
(
6
+
3
)
=
log
4
6
+
log
4
3
(iv)
log
2
(
25
3
)
=
log
2
25
log
2
3
(v)
log
1
3
3
=
−
1
(vi)
log
a
(
M
−
N
)
=
log
a
M
÷
log
a
N
Open in App
Solution
i
)
log
5
5
3
=
3
log
5
5
=
3
→
T
r
u
e
i
i
)
log
1
2
8
=
log
2
−
1
2
3
=
3
−
1
log
2
2
=
−
3
→
F
a
l
s
e
i
i
i
)
log
4
(
6
+
3
)
=
log
4
6
+
log
4
3
→
F
a
l
s
e
Because
log
4
6
+
log
4
3
=
log
4
(
6.3
)
i
v
)
log
2
(
25
3
)
=
log
2
25
log
2
3
→
F
a
l
s
e
v
)
log
1
3
3
=
log
3
−
1
3
=
−
1
→
T
r
u
e
v
i
)
log
a
(
M
−
N
)
=
log
a
M
÷
log
a
N
→
F
a
l
s
e
Suggest Corrections
0
Similar questions
Q.
The value of
log
4
81
log
4
3
−
log
2
16
log
2
4
is:
Q.
Solve the equation in each of the following.
(i)
log
4
(
x
+
4
)
+
log
4
8
=
2
(ii)
log
6
(
x
+
4
)
−
log
6
(
x
−
1
)
=
1
(iii)
log
2
x
+
log
4
x
+
log
8
x
=
11
6
(iv)
log
4
(
8
log
2
x
)
=
2
(v)
log
10
5
+
log
10
(
5
x
+
1
)
=
log
10
(
x
+
5
)
+
1
(vi)
4
log
2
x
−
log
2
5
=
log
2
125
(vii)
log
3
25
+
log
3
x
=
3
log
3
5
(viii)
log
3
(
√
5
x
−
2
)
−
1
2
=
log
3
(
√
x
+
4
)
Q.
Given
log
a
2
=
x
,
log
a
3
=
y
and
log
a
5
=
z
. Find the value in each of the following in terms of
x
,
y
and
z
.
(i)
log
a
15
(ii)
log
a
8
(iii)
log
a
30
(iv)
log
a
(
27
125
)
(v)
log
a
(
3
1
3
)
(vi)
log
a
1.5
Q.
Number of solutions of
log
4
(
x
−
1
)
=
log
2
(
x
−
3
)
Q.
Solve the following equations.
(i)
log
2
x
=
1
2
(ii)
log
1
5
x
=
3
(iii)
log
3
y
=
−
2
(iv)
log
x
125
√
5
=
7
(v)
log
x
0.001
=
−
3
(vi)
x
+
2
log
27
9
=
0
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