Using the LAMBERT W FUNCTION find ALL solutions! / ( W_0 and W_-1)

In this video we are going to solve 2 equations using the Lambert W Function. The goal is to find all real solutions using the lambert w function. You will learn how to determine how many solutions should you get considering just the lambert w function. (without the graph)

Timecodes
0:00 - Intro
0:10 - introduction
2:52 - explaining two ways of solving the equation solve x^2=2^x,solve
3:02 - solving x^2=2^x for x greater than 0
5:52 - explaining how many solutions should we get using just the lambert W Function
8:59 - explaining all possible solution for x greater than 0 , for both branches W_0 and W_-1
10:57 - how to get expression for x considering the branch W_-1
15:30 - solving for x is less than 0
21:50 - solving the equation 2^x = 10x
24:50 - begging for subscribers :D

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[adrianirias]

Before you there were a few videos with such a broad approach to the topic regarding the Lambert function.I am a tutor for students who participate in math olympiads: I needed material in English to train them on that subject and thanks to you I am achieving it.I used videos in French( the French mathematical school gives a lot of attention to the subject).
In addition to the help provided, your didactic approach is excellent.You are so kind!
P.D. Congrats for your hair!!!

[daniel-mircea]

Very concise and clear explanation. Thank you!

[noahzuniga]

these are nice videos, i remember searching lambert W function videos on youtube only a few years ago and finding very little information about it, but yours and a few other channels quite recently have posted very good about it. much appreciated! keep it up

[mcrow]

Thanks for all the work you put into making this video.

[osrevad]

Thank you. I was trying to solve this problem yesterday for fun. Never even heard of Lambert W function before Wolfram Alpha gave me an answer. Thanks for the good explanation.

[stefanotonon]

Ottima spiegazione!
Grazie Ivana.
Grazie a te ripasso tanti concetti di matematica e fisica e imparo un pò l'inglese.

[ezio_g]

I thought I left a comment but I don't see it, maybe it was removed. My question is that at 15:36 for x<0 you replaced -x on the left side of the equation but not the right side and I wonder why?

[renesperb]

I would like to add the solutions of the case a^x=x ^n, with a>0 and n>0 : x1=Exp[-W[-ln [a] /n], x2= Exp[- W[-1, -ln [a]/n] ]
x3= - Exp[-W[ln[a]/n] .More than 2 solutions may arise if n is an even number.

[salvatorecosta]

A very nice lesson! OnceI was a mathematics teacher in an Italian high school but I never taught the Lambert function (which I barely knew). Is it normal to teach these things in the USA? Thanks for the reply.

[lanspire]

Cool, thanks for explaning how to solve different equations :D also good way to remind myself of wolfram functionalities :)

[hectortroncoso]

Really is sincerelly amazing;the clear of your way of teaching, thanks you.
Is very clear the way of your english; im from Argentina and mostly tutorials of other teachers in you tube, are very dfficult to understand for me;here we uses spanish, only, so to the difficulties natural of maths;it is added the difficulties of idiom, because of this ;i say thanks for all, mrs teacher.

[kwakuappiahduodu]

Nice video with easy to understand explanation. Please whenever I punch my question in Wolfram alpha I get Even.

[huzefa]

Thanks! Can you please share what are the real life applications of Lambert W function??

[rezakarimimoghaddam]

Thank you for this really helpful and precious content. During my research I contact a problem in the form of { A+Bx^C+DLn(Ex+F)=0} This probably should be solved by Lambert W Function. But I couldn't transform it into a solvable form of Lambert Function. My question is that, can the equations in the general form of {A+Bx^C+DLn(Ex^F+G)=0} be solved by Lambert W function? Thank you in advance for your response🙏

[naticc]

First of all, Thanks for a Perfect and detailed video!

But the only missing part here is:
How to calculate the W_-1, with formula/series?

I know there is a series for W_0.
But i didnt find any proper answer for W_-1 🥺

I'd be happy if you upload a video with a solution for finding the numerical value of
W_-1 🙏🏻

[rolandkaschek]

How do you know, that only the W_0 and W_(-1) have to be considered?

[mohanvaddadi]

X^2 = 2^x. ; Square root both sides ; x= 2^x/2; Now we can solve using W function

[SidneiMV]

hi friends. hi teacher

We know that W(xlnx) = lnx

And how about *W[(lnx)/x]* ?
Is there some "formula" in this case?

For example
We know W(17ln17) = ln17

But to find/calculate W[(ln17)/17], can we find an exact value, a perfect value, without using approximations, without using things like Wolfram Alpha?

[lanspire]

Also waiting for 1000 subs so we celebrate :D

[pixelninja]

Only 2 and 4 I guess in turns of integers