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x-log-2-x-256-




Question Number 193618 by Brianodhiambo last updated on 17/Jun/23
x^(log_2 x) =256
$${x}^{{log}_{\mathrm{2}} {x}} =\mathrm{256} \\ $$
Answered by aba last updated on 17/Jun/23
x^(log_2 (x)) =256 ⇒ x^(log_2 (x)) =2^8   ⇒log_2 ^2 x=log_2 2^8  ⇒ log_2 ^2 x=8 ⇒ log_2 x=±2(√2)  ⇒ x=2^(±2(√2))  ✓
$$\mathrm{x}^{\mathrm{log}_{\mathrm{2}} \left(\mathrm{x}\right)} =\mathrm{256}\:\Rightarrow\:\mathrm{x}^{\mathrm{log}_{\mathrm{2}} \left(\mathrm{x}\right)} =\mathrm{2}^{\mathrm{8}} \\ $$$$\Rightarrow\mathrm{log}_{\mathrm{2}} ^{\mathrm{2}} \mathrm{x}=\mathrm{log}_{\mathrm{2}} \mathrm{2}^{\mathrm{8}} \:\Rightarrow\:\mathrm{log}_{\mathrm{2}} ^{\mathrm{2}} \mathrm{x}=\mathrm{8}\:\Rightarrow\:\mathrm{log}_{\mathrm{2}} \mathrm{x}=\pm\mathrm{2}\sqrt{\mathrm{2}} \\ $$$$\Rightarrow\:\mathrm{x}=\mathrm{2}^{\pm\mathrm{2}\sqrt{\mathrm{2}}} \:\checkmark \\ $$

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