Question Number 152942 by mathlove last updated on 03/Sep/21
Commented by mathdanisur last updated on 03/Sep/21
$$\mathrm{8}\:=\:\mathrm{8}^{\boldsymbol{\mathrm{x}}} \:\Rightarrow\:\mathrm{x}\:=\:\mathrm{1} \\ $$
Answered by puissant last updated on 03/Sep/21
$$\mathrm{4}!=\mathrm{24}\:{and}\:\mathrm{4}!!=\mathrm{4}×\mathrm{2}=\mathrm{8} \\ $$$$\Rightarrow\:\frac{\mathrm{4}!}{\mathrm{4}!!}=\frac{\mathrm{24}}{\mathrm{8}}=\mathrm{3} \\ $$$$\mathrm{2}^{\frac{\mathrm{4}!}{\mathrm{4}!!}} =\mathrm{8}^{{x}} \:\Rightarrow\:\mathrm{8}=\mathrm{8}^{{x}} \:\Rightarrow\:{e}^{{ln}\mathrm{8}} ={e}^{{xln}\mathrm{8}} \\ $$$$\Rightarrow\:{ln}\mathrm{8}={xln}\mathrm{8}\: \\ $$$$\Rightarrow\:{x}=\mathrm{1}.. \\ $$
Commented by mathlove last updated on 03/Sep/21
$${thanks}\:{sir} \\ $$
Answered by talminator2856791 last updated on 03/Sep/21
$$\: \\ $$$$\:\mathrm{2}^{\frac{\mathrm{4}!}{\mathrm{4}!!}} \:=\:\mathrm{8}^{{x}} \\ $$$$\:\mathrm{2}^{\frac{\mathrm{4}!}{\mathrm{4}!!}} \:=\:\mathrm{2}^{\mathrm{3}{x}} \\ $$$$\:\mathrm{3}{x}\:=\:\frac{\mathrm{4}!}{\mathrm{4}!!} \\ $$$$\:{x}\:=\:\frac{\mathrm{4}!}{\mathrm{3}\centerdot\mathrm{4}!!} \\ $$$$\: \\ $$