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Question Number 160317 by quvonnn last updated on 27/Nov/21

Commented by quvonnn last updated on 27/Nov/21

$$\mathit{x}=?$$

Answered by MathsFan last updated on 27/Nov/21

$$x^{x^{20}}=\sqrt[\sqrt{2}]{2}$$$$x^{20}lnx=ln\sqrt[\sqrt{2}]{2}$$$$lnx\bullet e^{20lnx}=ln\sqrt[\sqrt{2}]{2}$$$$20lnx\bullet e^{20lnx}=20ln\sqrt[\sqrt{2}]{2}$$$$20lnx=w\left(20ln\sqrt[\sqrt{2}]{2}\right)$$$$lnx=\frac{w\left(20ln\sqrt[\sqrt{2}]{2}\right)}{20}$$$$x=e^{\frac{w\left(20ln\sqrt[\sqrt{2}]{2}\right)}{20}}$$$$$$

Commented by quvonnn last updated on 27/Nov/21

$$\mathit{w}=?$$

Commented by quvonnn last updated on 28/Nov/21

$$Youunderstand$$

Commented by quvonnn last updated on 28/Nov/21

$$w=????what$$

Commented by quvonnn last updated on 28/Nov/21

$$whatisthisconcept$$

Commented by quvonnn last updated on 28/Nov/21

$$ok.w\left(x\right).f\left(x\right)={xe}^x$$

Commented by mr W last updated on 28/Nov/21

$$W\left(x\right)standsforLambertWfunction,$$$$whichisdefinedastheinverse$$$$functionoff\left(x\right)={xe}^x.i.e.$$$$W\left(x\right)e^{W\left(x\right)}=x.$$

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