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National and Regional Contests
China Contests
(China) National High School Mathematics League
2011 China Second Round Olympiad
3
find log-a b
find log-a b
Source: China Second Round Test 1
January 30, 2012
logarithms
inequalities
algebra unsolved
algebra
Problem Statement
Let
a
,
b
a,b
a
,
b
be positive reals such that
1
a
+
1
b
≤
2
2
\frac{1}{a}+\frac{1}{b}\leq2\sqrt2
a
1
+
b
1
≤
2
2
and
(
a
−
b
)
2
=
4
(
a
b
)
3
(a-b)^2=4(ab)^3
(
a
−
b
)
2
=
4
(
ab
)
3
. Find
log
a
b
\log_a b
lo
g
a
b
.
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