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Swedish Mathematical Competition
2015 Swedish Mathematical Competition
4
logarithm 2x3 system
logarithm 2x3 system
Source: 2015 Swedish Mathematical Competition p4
April 30, 2021
algebra
system of equations
logarithm
System
logarithms
Problem Statement
Solve the system of equations
{
x
log
x
+
y
log
y
+
z
log
x
=
0
log
x
x
+
log
y
y
+
log
z
z
=
0
\left\{\begin{array}{l} x \log x+y \log y+z \log x=0\\ \\ \dfrac{\log x}{x}+\dfrac{\log y}{y}+\dfrac{\log z}{z}=0 \end{array} \right.
⎩
⎨
⎧
x
lo
g
x
+
y
lo
g
y
+
z
lo
g
x
=
0
x
lo
g
x
+
y
lo
g
y
+
z
lo
g
z
=
0
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