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Question Number 193618 by Brianodhiambo last updated on 17/Jun/23

$$x^{{log}_{2}x}=256$$

Answered by aba last updated on 17/Jun/23

$${\mathrm{x}}^{{\log }_2\left(\mathrm{x}\right)}=256\Rightarrow {\mathrm{x}}^{{\log }_2\left(\mathrm{x}\right)}=2^8$$$$\Rightarrow {\log }_2^2\mathrm{x}={\log }_2{2}^8\Rightarrow {\log }_2^2\mathrm{x}=8\Rightarrow {\log }_2\mathrm{x}=\pm 2\sqrt{2}$$$$\Rightarrow \mathrm{x}=2^{\pm 2\sqrt{2}}✓$$

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