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

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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