MathDB
Problems
Contests
National and Regional Contests
Romania Contests
District Olympiad
2014 District Olympiad
2
Another equation
Another equation
Source: Romanian District Olympiad 2014, Grade 10, P2
June 15, 2014
logarithms
algebra proposed
algebra
Problem Statement
Solve in real numbers the equation
x
+
log
2
(
1
+
5
x
3
x
+
4
x
)
=
4
+
log
1
/
2
(
1
+
2
5
x
7
x
+
2
4
x
)
x+\log_{2}\left( 1+\sqrt{\frac{5^{x}}{3^{x}+4^{x}}}\right) =4+\log_{1/2}\left(1+\sqrt{\frac{25^{x}}{7^{x}+24^{x}}}\right)
x
+
lo
g
2
(
1
+
3
x
+
4
x
5
x
)
=
4
+
lo
g
1/2
(
1
+
7
x
+
2
4
x
2
5
x
)
Back to Problems
View on AoPS