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Problems
Contests
National and Regional Contests
China Contests
(China) National High School Mathematics League
2006 China Second Round Olympiad
2
2006 China Second Round Olympiad Test 1 #2
2006 China Second Round Olympiad Test 1 #2
Source:
September 28, 2014
logarithms
Problem Statement
Suppose
l
o
g
x
(
2
x
2
+
x
−
1
)
>
l
o
g
x
2
−
1
log_x (2x^2+x-1)>log_x 2-1
l
o
g
x
(
2
x
2
+
x
−
1
)
>
l
o
g
x
2
−
1
. Then the range of
x
x
x
is
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
1
2
<
x
<
1
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
x
>
1
2
and
x
≠
1
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
x
>
1
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
0
<
x
<
1
{ <span class='latex-bold'>(A)</span>\ \frac{1}{2}<x<1\qquad<span class='latex-bold'>(B)</span>\ x>\frac{1}{2} \text{and} x \not= 1\qquad<span class='latex-bold'>(C)</span>\ x>1\qquad<span class='latex-bold'>(D)</span>}\ 0<x<1\qquad
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
2
1
<
x
<
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
x
>
2
1
and
x
=
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
x
>
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
0
<
x
<
1
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