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Moscow Mathematical Olympiad
2018 Moscow Mathematical Olympiad
7
Equation with logarithms
Equation with logarithms
Source: Moscow Olympiad 2018, Grade 11, P7
April 7, 2018
algebra
logarithms
Problem Statement
x
3
+
(
log
2
5
+
log
3
2
+
log
5
3
)
x
=
(
log
2
3
+
log
3
5
+
log
5
2
)
x
2
+
1
x^3+(\log_2{5}+\log_3{2}+\log_5{3})x=(\log_2{3}+\log_3{5}+\log_5{2})x^2+1
x
3
+
(
lo
g
2
5
+
lo
g
3
2
+
lo
g
5
3
)
x
=
(
lo
g
2
3
+
lo
g
3
5
+
lo
g
5
2
)
x
2
+
1
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