Question Number 145577 by mathlove last updated on 06/Jul/21
Commented by mr W last updated on 06/Jul/21
$${see}\:{Q}\mathrm{145256} \\ $$
Answered by puissant last updated on 06/Jul/21
$$\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\sqrt{\mathrm{2}}} =\:\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}} =\:\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{2}^{−\frac{\mathrm{1}}{\mathrm{4}}} } =\:\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\left(\frac{\mathrm{1}}{\mathrm{4}}\right)} } =\:\mathrm{x}^{\mathrm{x}^{\mathrm{x}} } \\ $$$$\Rightarrow\:\mathrm{x}=\frac{\mathrm{1}}{\mathrm{4}}. \\ $$
Answered by Rhidy last updated on 27/Dec/21
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