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All-Russian Olympiad Regional Round
1997 All-Russian Olympiad Regional Round
11.6
sum log_a(log_a b) > 0 - All-Russian MO 1997 Regional (R4) 11.6
sum log_a(log_a b) > 0 - All-Russian MO 1997 Regional (R4) 11.6
Source:
September 24, 2024
algebra
logarithm
inequalities
Problem Statement
Prove that if
1
<
a
<
b
<
c
1 < a < b < c
1
<
a
<
b
<
c
, then
log
a
(
log
a
b
)
+
log
b
(
log
b
c
)
+
log
c
(
log
c
a
)
>
0.
\log_a(\log_a b) + \log_b(\log_b c) + \log_c(\log_c a) > 0.
lo
g
a
(
lo
g
a
b
)
+
lo
g
b
(
lo
g
b
c
)
+
lo
g
c
(
lo
g
c
a
)
>
0.
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