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Question Number 100151 by student work last updated on 25/Jun/20

$$\sqrt{\mathrm{lnx}}-\ln \sqrt{\mathrm{x}}=0\mathrm{x}=?$$

Commented by bobhans last updated on 25/Jun/20

$$\mathrm{set}\sqrt{\ln \left(\mathrm{x}\right)}=\mathrm{u}$$$$\mathrm{u}-\frac{1}{2}{\mathrm{u}}^2=0\Rightarrow \frac{1}{2}\mathrm{u}(2-\mathrm{u})=0$$$$\{\begin{array}{l}\mathrm{u}=0\Rightarrow \ln \left(\mathrm{x}\right)=0,\mathrm{x}=1\\ \mathrm{u}=2\Rightarrow \ln \left(\mathrm{x}\right)=4,\mathrm{x}={\mathrm{e}}^4\end{array}$$$$$$

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