Question Number 139525 by TOTTI last updated on 28/Apr/21
Commented by mr W last updated on 29/Apr/21
$$=\mathrm{log}_{\sqrt{{x}}} \:\left(\sqrt{{x}}\right)^{\mathrm{2}} =\mathrm{3}^{\mathrm{1}/\mathrm{3}} \\ $$$$=\mathrm{2log}_{\sqrt{{x}}} \:\sqrt{{x}}=\mathrm{3}^{\mathrm{1}/\mathrm{3}} \\ $$$$\Rightarrow\mathrm{2}=\mathrm{3}^{\mathrm{1}/\mathrm{3}} \\ $$$${no}\:{solution}! \\ $$
Commented by SWPlaysMC last updated on 16/Dec/21
$${Agreed}. \\ $$
Commented by MJS_new last updated on 28/Apr/21
$$\mathrm{log}\:_{\sqrt{{x}}} \:{x}\:=\frac{\mathrm{ln}\:{x}}{\mathrm{ln}\:\sqrt{{x}}}=\frac{\mathrm{ln}\:{x}}{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:{x}}=\mathrm{2} \\ $$