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Problems
Contests
National and Regional Contests
China Contests
(China) National High School Mathematics League
2011 China Second Round Olympiad
9
functionproblem
functionproblem
Source: China Second Round Test1
January 30, 2012
logarithms
algebra unsolved
algebra
Problem Statement
Let
f
(
x
)
=
∣
log
(
x
+
1
)
∣
f(x)=|\log(x+1)|
f
(
x
)
=
∣
lo
g
(
x
+
1
)
∣
and let
a
,
b
a,b
a
,
b
be two real numbers (
a
<
b
a<b
a
<
b
) satisfying the equations
f
(
a
)
=
f
(
−
b
+
1
a
+
1
)
f(a)=f\left(-\frac{b+1}{a+1}\right)
f
(
a
)
=
f
(
−
a
+
1
b
+
1
)
and
f
(
10
a
+
6
b
+
21
)
=
4
log
2
f\left(10a+6b+21\right)=4\log 2
f
(
10
a
+
6
b
+
21
)
=
4
lo
g
2
. Find
a
,
b
a,b
a
,
b
.
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