Recently I have created this question:
$$(x+1)^xe^{x+1}=(2x)^x$$
And the solution
$$(x+1)^xe^{x+1}=(2x)^x$$$$(x+1)e^{1+\frac 1 x}=2x$$$$(1+\frac 1 x)e^{1+\frac 1 x}=2$$$$1+\frac 1 x=W(2)$$ $$x=\frac 1 {W(2)-1}$$
But Desmos shows no solution, can anyone explain what is wrong here?
Wolfy says the solution to $ze^z=2$ is about $z≈0.85260550201372549135$ so $x≈-6.7845137617899467654$.
The problem is defining the specified powers.