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Question Number 212123 by MrGaster last updated on 02/Oct/24

$$$$$$\mathrm{solve}\mathrm{an}\mathrm{equation}:$$$$\sqrt{\mathbf{ln}\mathit{x}}=\mathbf{ln}\sqrt{\mathit{x}}$$

Answered by Frix last updated on 02/Oct/24

$$\sqrt{\ln x}=\frac{\ln x}{2}$$$$2\sqrt{\ln x}-\ln x=0$$$$\sqrt{\ln x}(2-\sqrt{\ln x})=0$$$$\sqrt{\ln x}=0\vee \sqrt{\ln x}=2$$$$\ln x=0\vee \ln x=4$$$$x=1\vee x={\mathrm{e}}^4$$

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