How to solve $8x^2 = x \ln(x)$

Question

When does $8x^2$ outperform $x \ln(x)$ function. I found such problem in O(n) computations and had not found answer swiftly

Answer 1

$8x^2=x\ln(x)$

$8x=\ln(x)$

$e^{8x}=x$

$xe^{-8x}=1$

$-8xe^{-8x}=-8$

$-8x=W(-8)$ where $W$ is the Lambert W function.

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According to WolframAlpha, $W(-8) \approx 1.199\ldots + 2.091\ldots i$