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Question Number 212123 by MrGaster last updated on 02/Oct/24
                   solve an equation:                      (√(ln x))=ln(√x)
$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{solve}\:\mathrm{an}\:\mathrm{equation}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt{\boldsymbol{\mathrm{ln}}\:\boldsymbol{{x}}}=\boldsymbol{\mathrm{ln}}\sqrt{\boldsymbol{{x}}} \\ $$
Answered by Frix last updated on 02/Oct/24
(√(ln x))=((ln x)/2)  2(√(ln x))−ln x =0  (√(ln x))(2−(√(ln x)))=0  (√(ln x))=0∨(√(ln x))=2  ln x =0∨ln x =4  x=1∨x=e^4
$$\sqrt{\mathrm{ln}\:{x}}=\frac{\mathrm{ln}\:{x}}{\mathrm{2}} \\ $$$$\mathrm{2}\sqrt{\mathrm{ln}\:{x}}−\mathrm{ln}\:{x}\:=\mathrm{0} \\ $$$$\sqrt{\mathrm{ln}\:{x}}\left(\mathrm{2}−\sqrt{\mathrm{ln}\:{x}}\right)=\mathrm{0} \\ $$$$\sqrt{\mathrm{ln}\:{x}}=\mathrm{0}\vee\sqrt{\mathrm{ln}\:{x}}=\mathrm{2} \\ $$$$\mathrm{ln}\:{x}\:=\mathrm{0}\vee\mathrm{ln}\:{x}\:=\mathrm{4} \\ $$$${x}=\mathrm{1}\vee{x}=\mathrm{e}^{\mathrm{4}} \\ $$

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