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Question Number 170661 by solomonwells last updated on 28/May/22

$$\mathbf{log}{}^3\sqrt{}\mathbf{x}=\sqrt{\mathbf{logx}}$$$$\mathbf{solve}\mathbf{for}\mathit{X}$$$$$$

Commented by kaivan.ahmadi last updated on 28/May/22

$$\frac{1}{3}logx={\left(logx\right)}^{\frac{1}{2}}$$$$y={\left(logx\right)}^{\frac{1}{2}}$$$$\frac{1}{3}{y}^2=y\Rightarrow y^2-3y=0\Rightarrow y=0,y=3$$$$ify=0\Rightarrow {\left(logx\right)}^{\frac{1}{2}}=0\Rightarrow logx=0\Rightarrow x=1$$$$ify=3\Rightarrow {\left(logx\right)}^{\frac{1}{2}}=3\Rightarrow logx=9\Rightarrow x={10}^9$$

Commented by solomonwells last updated on 28/May/22

$$\mathrm{thanks}\mathrm{sir}$$

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