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Jozsef Wildt International Math Competition
2019 Jozsef Wildt International Math Competition
W. 4
Prove this inequality on logarithms
Prove this inequality on logarithms
Source: 2019 Jozsef Wildt International Math Competition-W. 4
May 18, 2020
inequalities
logarithms
Problem Statement
If
x
,
y
,
z
,
t
>
1
x, y, z, t > 1
x
,
y
,
z
,
t
>
1
then:
(
log
z
x
t
x
)
2
+
(
log
x
y
t
y
)
2
+
(
log
x
y
z
z
)
2
+
(
log
y
z
t
t
)
2
>
1
4
\left(\log _{zxt}x\right)^2+\left(\log _{xyt}y\right)^2+\left(\log _{xyz}z\right)^2+\left(\log _{yzt}t\right)^2>\frac{1}{4}
(
lo
g
z
x
t
x
)
2
+
(
lo
g
x
y
t
y
)
2
+
(
lo
g
x
yz
z
)
2
+
(
lo
g
yz
t
t
)
2
>
4
1
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