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Byju's Answer
Standard IX
Mathematics
Property 4
Prove that ...
Question
Prove that
a
x
−
b
y
=
0
where
x
=
√
log
a
b
&
y
=
√
log
b
a
,
a
>
0
,
b
>
0
&
a
,
b
≠
1
Open in App
Solution
Now,
a
x
−
b
y
=
0
⇒
a
x
=
b
y
x
=
√
log
b
a
,
y
=
√
log
a
b
x
y
=
√
log
b
a
log
a
b
=
√
(
log
b
a
)
2
x
y
=
log
b
a
b
=
a
x
y
b
y
=
a
x
S
o
,
a
x
−
b
y
=
0
Suggest Corrections
0
Similar questions
Q.
Prove that
a
x
−
b
y
=
0
where
x
=
√
log
a
b
and
y
=
√
log
b
a
,
a
>
0
,
b
>
0
and
a
,
b
≠
1
.
Q.
Prove that
a
x
−
b
y
=
0
where
x
=
√
log
a
b
&
y
=
√
log
b
a
,
a
>
0
,
b
>
0
&
a
,
b
≠
1
Q.
Prove
log
b
a
×
log
a
b
=
1
.
Q.
Find the minimum value of
l
o
g
a
b
+
l
o
g
b
a
(where a and b are not equal to 1).
Q.
Prove the following :
∣
∣ ∣ ∣ ∣
∣
0
x
y
z
−
x
0
c
b
−
y
−
c
0
a
−
z
−
b
−
a
0
∣
∣ ∣ ∣ ∣
∣
=
(
a
x
−
b
y
+
c
z
)
2
.
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