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Byju's Answer
Standard XII
Mathematics
Fundamental Laws of Logarithms
If 1/loga x+1...
Question
If
1
l
o
g
a
x
+
1
l
o
g
c
x
=
2
l
o
g
b
x
, then a,b,c are in
A
A.P.
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B
G.P.
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C
H.P.
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D
None of these
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Solution
The correct option is
B
G.P.
l
o
g
x
a
+
l
o
g
x
x
=
2
l
o
g
x
b
⇒
a
c
=
b
2
Suggest Corrections
2
Similar questions
Q.
If a,b,c are distinct positive numbers each different from 1 such that
[
l
o
g
b
a
l
o
g
c
a
−
l
o
g
a
a
]
+
[
l
o
g
a
b
l
o
g
c
b
−
l
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b
b
]
+
[
l
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a
c
l
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b
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−
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c
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]
=
0
then abc
Q.
If
a
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b
,
c
are in GP
(
a
>
1
,
b
>
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,
c
>
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)
, then for any real number
x
(with
x
>
0
,
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≠
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),
log
a
x
,
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b
x
,
log
c
x
are in
Q.
If a, b, c are distinct positive numbers, each different from 1, such that
[
l
o
g
b
a
l
o
g
c
a
−
l
o
g
a
a
]
+
[
l
o
g
a
b
l
o
g
c
b
−
l
o
g
b
b
]
+
[
l
o
g
a
c
l
o
g
b
c
−
l
o
g
c
c
]
=
0
,
t
h
e
n
a
b
c
=
Q.
If
log
(
a
b
−
c
)
=
log
(
b
c
−
a
)
=
log
(
c
a
−
b
)
then
a
a
×
b
b
×
c
c
=
1
Q.
If
a
,
b
,
c
are in GP, then
log
a
,
log
b
,
log
c
are in
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