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Byju's Answer
Standard XII
Mathematics
Conditions on the Parameters of Logarithm Function
The number of...
Question
The number of real values of
x
,
satisfying
3
2
log
3
x
−
2
x
−
3
=
0
is
A
0
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B
1
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C
2
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D
more than
2
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Solution
The correct option is
B
1
3
2
log
3
x
−
2
x
−
3
=
0
For the
log
to be defined,
x
>
0
⋯
(
1
)
Now,
3
log
3
x
2
−
2
x
−
3
=
0
⇒
x
2
−
2
x
−
3
=
0
(
∵
a
log
a
b
=
b
)
⇒
(
x
−
3
)
(
x
+
1
)
=
0
∴
x
=
3
(
∵
x
>
0
)
Hence, there is only one solution of the given equation.
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