2^x =4x ⇒ (x/2^x )=(1/4) ⇒x.e^(−ln(2^x )) =(1/4) ⇒−xln(2)e^(−ln(2x)) =−(1/4)ln(2) ⇒W(−ln(2^x )e^(−ln(2^x )) )=W(−(1/4)ln(2)) ⇒−ln(2^x )=W(−(1/4)ln(2)) ⇒x=−((W(−(1/4)ln(2)) )/(ln(2))) =((W(−(1/2^4 )ln(2^4 )))/(ln(2))) ⇒x=−((W(−ln(2^4 )e^(−ln(2^4 )) ))/(ln(2))) ⇒x=((ln(2^4 ))/(ln(2))) ⇒x=4


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Question Number 185075 by aba last updated on 16/Jan/23

$2^{x} = 4 x \Rightarrow \frac{x}{2^{x}} = \frac{1}{4}$ $\Rightarrow x . e^{- \ln (2^{x})} = \frac{1}{4}$ $\Rightarrow - xln (2) e^{- \ln (2 x)} = - \frac{1}{4} \ln (2)$ $\Rightarrow W (- \ln (2^{x}) e^{- \ln (2^{x})}) = W (- \frac{1}{4} \ln (2))$ $\Rightarrow - \ln (2^{x}) = W (- \frac{1}{4} \ln (2))$ $\Rightarrow x = - \frac{W (- \frac{1}{4} \ln (2))}{\ln (2)} = \frac{W (- \frac{1}{2^{4}} \ln (2^{4}))}{\ln (2)}$ $\Rightarrow x = - \frac{W (- \ln (2^{4}) e^{- \ln (2^{4})})}{\ln (2)}$ $\Rightarrow x = \frac{\ln (2^{4})}{\ln (2)}$ $\Rightarrow x = 4$
Commented by Frix last updated on 16/Jan/23

$I gave the answer in question 184989$
Commented by aba last updated on 16/Jan/23

$yes i know$
Commented by Frix last updated on 16/Jan/23

$Then {where}^{'} s the 2^{nd} solution ?$
Commented by aba last updated on 16/Jan/23

$?!$
Commented by Frix last updated on 16/Jan/23

$x \approx . 309907$
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