(untitled)

e$^x$x = x$^\pi$, what is x?

$\small{ \begin{array}{rcll} e^x &=& x^{\pi} \qquad & | \qquad \ln{}\\ x\ln{(e)} &=& \pi \cdot \ln{(x)} \\ \frac{x}{\pi} \cdot \ln{(e)}&=& \ln{(x)} \\ \ln{( e^{\frac{x}{\pi}} )} &=& \ln{(x)} \qquad & | \qquad e^{}\\ e^{ \ln{( e^{\frac{x}{\pi}} )} } &=& e^{ \ln{(x)} }\\ e^{\frac{x}{\pi}} &=& x \\ x \cdot e^{-\frac{x}{\pi}} &=& 1 \qquad & | \qquad : -\pi\\ -\frac{x}{\pi} \cdot e^{-\frac{x}{\pi}} &=& -\frac{1}{\pi}\\ \\ \hline \end{array} }\\ \small{ \begin{array}{rcll} \text{Lambert W-Function(W) or ProductLog or Omega-Function } w\cdot e^w = z \qquad w = W(z) \end{array} }\\ \small{ \begin{array}{rcl} -\frac{x}{\pi} \cdot e^{-\frac{x}{\pi}} &=& -\frac{1}{\pi} \\ -\frac{x}{\pi} &=& W( -\frac{1}{\pi} ) \\ -x &=& \pi \cdot W( -\frac{1}{\pi} )\\ \mathbf{x} & \mathbf{=} & \mathbf{-\pi \cdot W( -\frac{1}{\pi} )}\\ \\ \hline \\ W( -\frac{1}{\pi} ) &=& -0.553827036644513 \\ x &=& -\pi \cdot (-0.553827036644513) \\ \mathbf{ x } & \mathbf{\approx} & \mathbf{1.73989894968181} \\ \end{array} }\\$