Question Number 226830 by Estevao last updated on 16/Dec/25
Answered by TonyCWX last updated on 17/Dec/25
$$\mathrm{27}\:=\:\mathrm{3}^{\mathrm{3}} \:=\:^{\mathrm{2}} \mathrm{3} \\ $$$$\:^{\mathrm{2}} {x}\:=\:\mathrm{2} \\ $$$${x}^{{x}} =\mathrm{2} \\ $$$$\mathrm{For}\:{x}^{{x}} ={a},\:{x}={e}^{{W}\left(\mathrm{ln}\left(\mathrm{2}\right)\right)} ,\:\mathrm{where}\:{W}\left({x}\right)\:=\:\mathrm{Lambert}\:\mathrm{W}\:\mathrm{Function} \\ $$$${x}\:=\:{e}^{{W}\left(\mathrm{ln}\left(\mathrm{2}\right)\right)} \\ $$