Solving Exponential Equation (using Lambert W function)

[mtc-ji]

I don’t understand the step where you put parentheses around everything and then put a “ -1” outside. What were you doing in that step exactly?

[pauselab]

I mean it's just a definition if you can't actually compute W(x) as a function. maybe there is a taylor series or something or useful because this feels like defining random stuff. (though it does have a wikipedia page so guess imma go read that)

[odio_stationofficial]

That is not final answer...the final answer should be *e^W(ln2)* instead of e^(-W(ln(0.5)))...
You left it there, it's now driving me crazy 🐺😡

[vjbibct]

So.... the solution is, there are no real solutions. You would have to square the equation in order for any hope at a real solution. Right, wrong?

[rufusmafija]

how can you calculate the w function(its not on calculator or photomath)

[andersmhc]

2^x=x
(e^ln(2))^x=x
e^(xln(2))=x

Multiply both sides with e^-xln(2)
1=xe^(-xln(2))

Multiply both sides with -ln(2)
-ln(2)=-xln(2)e^(-xln(2))

Take the Lambert W function on both sides:
W(-ln(2))=-xln(2)

x=-W(-ln(2))/ln(2)

[klm]

I got x = (W(ln(2))/(ln(2)), where did I go wrong?

[pierrettebalazut]

OH, il n ' y a pas à hésiter....je révise les logarithmes et exponentielles....
Et après ce sera les imaginaires.... il y a du boulot sur la planche !