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Byju's Answer
Standard X
Mathematics
Arithmetic Progression
If P denote...
Question
If
P
denotes the product of all the values of
x
satisfying
log
3
x
3
x
+
(
log
3
x
)
2
=
1
, then find
18
P
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Solution
log
3
x
3
x
+
(
log
3
x
)
2
=
1
Clearly
x
>
0
log
3
3
x
log
3
(
3
x
)
+
(
log
3
x
)
2
=
1
[
∵
log
b
a
=
log
a
log
b
]
⇒
log
3
3
−
log
x
log
3
3
+
log
3
x
+
(
log
3
x
)
2
=
1
Put
t
=
log
3
x
to obtain
1
−
t
1
+
t
+
t
2
=
1
[
∵
log
a
a
=
1
]
⇒
t
3
+
t
2
−
2
t
=
0
⇒
t
(
t
2
+
t
−
2
)
=
0
⇒
t
(
(
t
−
1
)
(
t
+
2
)
)
=
0
⇒
t
=
0
,
1
,
−
2
∴
x
=
3
0
,
3
1
,
3
−
2
x
=
1
,
3
,
1
9
⇒
P
=
1
9
×
1
×
3
⇒
P
=
1
3
⇒
18
P
=
18
3
=
6
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Similar questions
Q.
If
P
is product of all the values of
x
satisfying the equation
log
2
x
2
−
1
(
x
2
−
2
3
)
−
2
=
−
1
log
3
(
2
x
2
−
1
)
, then find
4
|
P
|
.
Q.
After evaluating
log
3
x
+
log
3
x
=
log
√
3
x
+
log
3
√
x
+
1
2
, value of
x
will be
Q.
The value of
x
satisfying
log
3
4
−
2
log
3
√
3
x
+
1
=
1
−
log
3
(
5
x
−
2
)
is:
Q.
The set of all x satisfying the equation
x
log
3
x
2
+
(
log
3
x
)
2
−
10
=
1
x
2
Q.
If
P
and
Q
are the sum and product respectively of all integral values of
x
satisfying the equation
|
3
[
x
]
−
4
x
|
=
4
, then
(where [.] denotes represents greatest integer function )
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