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Question Number 6838 by Tawakalitu. last updated on 30/Jul/16
Find the value of x  4^x  = ((243)/x)
$${Find}\:{the}\:{value}\:{of}\:{x} \\ $$$$\mathrm{4}^{{x}} \:=\:\frac{\mathrm{243}}{{x}} \\ $$
Commented by Yozzii last updated on 31/Jul/16
4^x =((243)/x)  xe^(xln4) =243  (xln4)e^(xln4) =243ln4  ⇒W((xln4)e^(xln4) )=W(243ln4)  ⇒xln4=W(243ln4)  x=((W(243ln4))/(ln4))≈3.14
$$\mathrm{4}^{{x}} =\frac{\mathrm{243}}{{x}} \\ $$$${xe}^{{xln}\mathrm{4}} =\mathrm{243} \\ $$$$\left({xln}\mathrm{4}\right){e}^{{xln}\mathrm{4}} =\mathrm{243}{ln}\mathrm{4} \\ $$$$\Rightarrow{W}\left(\left({xln}\mathrm{4}\right){e}^{{xln}\mathrm{4}} \right)={W}\left(\mathrm{243}{ln}\mathrm{4}\right) \\ $$$$\Rightarrow{xln}\mathrm{4}={W}\left(\mathrm{243}{ln}\mathrm{4}\right) \\ $$$${x}=\frac{{W}\left(\mathrm{243}{ln}\mathrm{4}\right)}{{ln}\mathrm{4}}\approx\mathrm{3}.\mathrm{14} \\ $$
Commented by Tawakalitu. last updated on 31/Jul/16
i really appreciate.
$${i}\:{really}\:{appreciate}.\: \\ $$

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