Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

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

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

$$ \\ $$$$\mathrm{2}^{\mathrm{x}} =\mathrm{4x}\:\Rightarrow\:\:\frac{\mathrm{x}}{\mathrm{2}^{\mathrm{x}} }=\frac{\mathrm{1}}{\mathrm{4}}\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\mathrm{x}.\mathrm{e}^{−\mathrm{ln}\left(\mathrm{2}^{\mathrm{x}} \right)} =\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow−\mathrm{xln}\left(\mathrm{2}\right)\mathrm{e}^{−\mathrm{ln}\left(\mathrm{2x}\right)} =−\frac{\mathrm{1}}{\mathrm{4}}\mathrm{ln}\left(\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\mathrm{W}\left(−\mathrm{ln}\left(\mathrm{2}^{\mathrm{x}} \right)\mathrm{e}^{−\mathrm{ln}\left(\mathrm{2}^{\mathrm{x}} \right)} \right)=\mathrm{W}\left(−\frac{\mathrm{1}}{\mathrm{4}}\mathrm{ln}\left(\mathrm{2}\right)\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow−\mathrm{ln}\left(\mathrm{2}^{\mathrm{x}} \right)=\mathrm{W}\left(−\frac{\mathrm{1}}{\mathrm{4}}\mathrm{ln}\left(\mathrm{2}\right)\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\mathrm{x}=−\frac{\mathrm{W}\left(−\frac{\mathrm{1}}{\mathrm{4}}\mathrm{ln}\left(\mathrm{2}\right)\right)\:\:}{\mathrm{ln}\left(\mathrm{2}\right)}\:=\frac{\mathrm{W}\left(−\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{4}} }\mathrm{ln}\left(\mathrm{2}^{\mathrm{4}} \right)\right)}{\mathrm{ln}\left(\mathrm{2}\right)} \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\mathrm{x}=−\frac{\mathrm{W}\left(−\mathrm{ln}\left(\mathrm{2}^{\mathrm{4}} \right)\mathrm{e}^{−\mathrm{ln}\left(\mathrm{2}^{\mathrm{4}} \right)} \right)}{\mathrm{ln}\left(\mathrm{2}\right)}\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\mathrm{x}=\frac{\mathrm{ln}\left(\mathrm{2}^{\mathrm{4}} \right)}{\mathrm{ln}\left(\mathrm{2}\right)} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\mathrm{x}=\mathrm{4} \\ $$

Commented by Frix last updated on 16/Jan/23

I gave the answer in question 184989

$$\mathrm{I}\:\mathrm{gave}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{question}\:\mathrm{184989} \\ $$

Commented by aba last updated on 16/Jan/23

yes i know

$$\mathrm{yes}\:\mathrm{i}\:\mathrm{know} \\ $$

Commented by Frix last updated on 16/Jan/23

Then where′s the 2^(nd) solution?

$$\mathrm{Then}\:\mathrm{where}'\mathrm{s}\:\mathrm{the}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{solution}? \\ $$

Commented by aba last updated on 16/Jan/23

?!

$$?! \\ $$

Commented by Frix last updated on 16/Jan/23

x≈.309907

$${x}\approx.\mathrm{309907} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com