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2000 Moldova National Olympiad
Problem 2
log inequality
log inequality
Source: Moldova 2000 Grade 10 P2
April 26, 2021
Inequality
inequalities
Problem Statement
Show that if real numbers
x
<
1
<
y
x<1<y
x
<
1
<
y
satisfy the inequality
2
log
x
+
log
(
1
−
x
)
≥
3
log
y
+
log
(
y
−
1
)
,
2\log x+\log(1-x)\ge3\log y+\log(y-1),
2
lo
g
x
+
lo
g
(
1
−
x
)
≥
3
lo
g
y
+
lo
g
(
y
−
1
)
,
then
x
3
+
y
3
<
2
x^3+y^3<2
x
3
+
y
3
<
2
.
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