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Question Number 139525 by TOTTI last updated on 28/Apr/21

Commented by mr W last updated on 29/Apr/21

=log_(√x)  ((√x))^2 =3^(1/3)   =2log_(√x)  (√x)=3^(1/3)   ⇒2=3^(1/3)   no solution!

$$=\mathrm{log}_{\sqrt{{x}}} \:\left(\sqrt{{x}}\right)^{\mathrm{2}} =\mathrm{3}^{\mathrm{1}/\mathrm{3}} \\ $$$$=\mathrm{2log}_{\sqrt{{x}}} \:\sqrt{{x}}=\mathrm{3}^{\mathrm{1}/\mathrm{3}} \\ $$$$\Rightarrow\mathrm{2}=\mathrm{3}^{\mathrm{1}/\mathrm{3}} \\ $$$${no}\:{solution}! \\ $$

Commented by SWPlaysMC last updated on 16/Dec/21

Agreed.

$${Agreed}. \\ $$

Commented by MJS_new last updated on 28/Apr/21

log _(√x)  x =((ln x)/(ln (√x)))=((ln x)/((1/2)ln x))=2

$$\mathrm{log}\:_{\sqrt{{x}}} \:{x}\:=\frac{\mathrm{ln}\:{x}}{\mathrm{ln}\:\sqrt{{x}}}=\frac{\mathrm{ln}\:{x}}{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:{x}}=\mathrm{2} \\ $$

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