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Question Number 152942 by mathlove last updated on 03/Sep/21

Commented by mathdanisur last updated on 03/Sep/21

8 = 8^x  ⇒ x = 1

$$\mathrm{8}\:=\:\mathrm{8}^{\boldsymbol{\mathrm{x}}} \:\Rightarrow\:\mathrm{x}\:=\:\mathrm{1} \\ $$

Answered by puissant last updated on 03/Sep/21

4!=24 and 4!!=4×2=8  ⇒ ((4!)/(4!!))=((24)/8)=3  2^((4!)/(4!!)) =8^x  ⇒ 8=8^x  ⇒ e^(ln8) =e^(xln8)   ⇒ ln8=xln8   ⇒ x=1..

$$\mathrm{4}!=\mathrm{24}\:{and}\:\mathrm{4}!!=\mathrm{4}×\mathrm{2}=\mathrm{8} \\ $$$$\Rightarrow\:\frac{\mathrm{4}!}{\mathrm{4}!!}=\frac{\mathrm{24}}{\mathrm{8}}=\mathrm{3} \\ $$$$\mathrm{2}^{\frac{\mathrm{4}!}{\mathrm{4}!!}} =\mathrm{8}^{{x}} \:\Rightarrow\:\mathrm{8}=\mathrm{8}^{{x}} \:\Rightarrow\:{e}^{{ln}\mathrm{8}} ={e}^{{xln}\mathrm{8}} \\ $$$$\Rightarrow\:{ln}\mathrm{8}={xln}\mathrm{8}\: \\ $$$$\Rightarrow\:{x}=\mathrm{1}.. \\ $$

Commented by mathlove last updated on 03/Sep/21

thanks sir

$${thanks}\:{sir} \\ $$

Answered by talminator2856791 last updated on 03/Sep/21

    2^((4!)/(4!!))  = 8^x    2^((4!)/(4!!))  = 2^(3x)    3x = ((4!)/(4!!))   x = ((4!)/(3∙4!!))

$$\: \\ $$$$\:\mathrm{2}^{\frac{\mathrm{4}!}{\mathrm{4}!!}} \:=\:\mathrm{8}^{{x}} \\ $$$$\:\mathrm{2}^{\frac{\mathrm{4}!}{\mathrm{4}!!}} \:=\:\mathrm{2}^{\mathrm{3}{x}} \\ $$$$\:\mathrm{3}{x}\:=\:\frac{\mathrm{4}!}{\mathrm{4}!!} \\ $$$$\:{x}\:=\:\frac{\mathrm{4}!}{\mathrm{3}\centerdot\mathrm{4}!!} \\ $$$$\: \\ $$

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