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National High School Mathematics League
1991 National High School Mathematics League
15
Inequality
Inequality
Source: 1991 National High School Mathematics League, Exam One, Problem 15
February 26, 2020
inequalities
Problem Statement
If
0
<
a
<
1
,
x
2
+
y
=
0
0<a<1,x^2+y=0
0
<
a
<
1
,
x
2
+
y
=
0
, prove that
log
a
(
a
x
+
a
y
)
≤
log
a
2
+
1
8
\log_a(a^x+a^y)\leq\log_a2+\frac{1}{8}
lo
g
a
(
a
x
+
a
y
)
≤
lo
g
a
2
+
8
1
.
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