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P1
Romania District MO 2022 Grade 10 P1
Romania District MO 2022 Grade 10 P1
Source: Romania District MO 2022 Grade 10
March 28, 2022
romania
logarithms
algebra
Problem Statement
Determine all
x
∈
(
0
,
3
/
4
)
x\in(0,3/4)
x
∈
(
0
,
3/4
)
which satisfy
log
x
(
1
−
x
)
+
log
2
1
−
x
x
=
1
(
log
2
x
)
2
.
\log_x(1-x)+\log_2\frac{1-x}{x}=\frac{1}{(\log_2x)^2}.
lo
g
x
(
1
−
x
)
+
lo
g
2
x
1
−
x
=
(
lo
g
2
x
)
2
1
.
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