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lambert W function solution for $x^2e^x=b$$\ln x=a+bx^{-1}$

Is is possible to solve the equation $x^2e^x=b$$\ln x=a+bx^{-1}$ using the Lambert W function? I understand that the lambert W function is the solution for equations like $xe^x=b$$\ln x=bx^{-1}$, which does not apply here.

lambert W function solution for $x^2e^x=b$

Is is possible to solve the equation $x^2e^x=b$ using the Lambert W function? I understand that the lambert W function is the solution for equations like $xe^x=b$, which does not apply here.

lambert W function solution for $\ln x=a+bx^{-1}$

Is is possible to solve the equation $\ln x=a+bx^{-1}$ using the Lambert W function? I understand that the lambert W function is the solution for equations like $\ln x=bx^{-1}$, which does not apply here.

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lambert W function solution for $x^2e^x=b$

Is is possible to solve the equation $x^2e^x=b$ using the Lambert W function? I understand that the lambert W function is the solution for equations like $xe^x=b$, which does not apply here.