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Byju's Answer
Standard IX
Mathematics
Property 6
If 2x4=y4+z...
Question
If
2
x
4
=
y
4
+
z
4
,
x
y
z
=
8
and
l
o
g
y
x
,
l
o
g
z
y
,
l
o
g
x
z
are in
G
.
P
.
, then find the value of
x
,
y
,
z
belonging to
R
.
Open in App
Solution
(
l
o
g
z
y
)
2
=
(
l
o
g
y
x
)
(
l
o
g
x
z
)
or
(
l
o
g
y
l
o
g
z
)
2
=
l
o
g
x
l
o
g
y
,
l
o
g
z
l
o
g
x
or
(
l
o
g
y
)
3
=
(
l
o
g
z
)
3
∴
y
=
z
.
∴
2
x
4
=
2
y
4
∴
x
=
y
=
z
Also
x
y
z
=
8
⇒
x
3
=
8
∴
x
=
2
=
y
=
z
.
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0
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