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2005 Croatia National Olympiad
3
inequality for logarit
inequality for logarit
Source: Croatian NMC 2005, 2nd Grade
May 8, 2007
inequalities
logarithms
inequalities proposed
Problem Statement
If
a
,
b
,
c
a, b, c
a
,
b
,
c
are real numbers greater than
1
1
1
, prove that for any real number
r
r
r
(
log
a
b
c
)
r
+
(
log
b
c
a
)
r
+
(
log
c
a
b
)
r
≥
3
⋅
2
r
.
(\log_{a}bc)^{r}+(\log_{b}ca)^{r}+(\log_{c}ab)^{r}\geq 3 \cdot 2^{r}.
(
lo
g
a
b
c
)
r
+
(
lo
g
b
c
a
)
r
+
(
lo
g
c
ab
)
r
≥
3
⋅
2
r
.
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