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x*lnx-x*lny equation

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Numerical solution:

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The solution

You have entered [src] 
x*log(x) - x*log(y) = 0
xlog⁡(x)−xlog⁡(y)=0x \log{\left(x \right)} - x \log{\left(y \right)} = 0
Simplify
The graph
Rapid solution [src] 
x1 = I*im(y) + re(y)
x1=re⁡(y)+iim⁡(y)x_{1} = \operatorname{re}{\left(y\right)} + i \operatorname{im}{\left(y\right)} 
x1 = re(y) + i*im(y)
Sum and product of roots [src] 
sum
I*im(y) + re(y)
re⁡(y)+iim⁡(y)\operatorname{re}{\left(y\right)} + i \operatorname{im}{\left(y\right)} 
=
I*im(y) + re(y)
re⁡(y)+iim⁡(y)\operatorname{re}{\left(y\right)} + i \operatorname{im}{\left(y\right)} 
product
I*im(y) + re(y)
re⁡(y)+iim⁡(y)\operatorname{re}{\left(y\right)} + i \operatorname{im}{\left(y\right)} 
=
I*im(y) + re(y)
re⁡(y)+iim⁡(y)\operatorname{re}{\left(y\right)} + i \operatorname{im}{\left(y\right)} 
i*im(y) + re(y)
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