Lambert W function

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Hi everyone, in this video, I will show you how to solve this kind of math problem by simply apply the Lambert w function. The Lambert w function is also known as the product log which is well explained here also.
In this lecture, I will show when and when not to use the Lambert w function solving tough exponential equations of this format.
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• Lambert W function
Below are few of the links to some of the video clip solved applying the Lambert w function.
1. Using Lambert w function to solve... • Solve x^5=4^x.
2. Olympiad algebra .... • Olympiad Algebra Quest...
3. Lambert w function and it's application... • Lambert W Function And...
4. How to solve exponential equation.... • How To Solve Exponenti...
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#lambert #maths #onlinemathstv

Опубликовано:

29 сен 2024

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Комментарии : 26

@Nikos_Iosifidis 8 месяцев назад

The equation was not completely solved. There is one more solution. Since the number (-ln4)/8 belongs to the interval (-1/e , 0) the Lambert function W_-1 must also be applied which gives the solution x = 0.15495 For more details and the complete solution of the equation x^x=a see my channel named L+M=N at: www.youtube.com/@Nikos_Iosifidis/videos The solution of the equation x^x =a is at: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-f8jmmnfu7wA.html I'd love for you to subscribe and comment on the topics I present.

@JacekWroński-u2z 8 месяцев назад

To be precise, the value of the argument of Lambert's W function is equal to -ln(4)/8=0.1733, the value of W=-0.2148, and x=-W/ln(4)=0.1550

@HalifaxHercules 8 месяцев назад

I also calculated the LambertW function result using WolframAlpha's Productlog function, and I got the same answer.

@Nikos_Iosifidis 8 месяцев назад

See my comment

@woncolee8848 4 месяца назад

搞了那麼多根本看不懂的鬼東西，還不如我的直接心算x=2

@Effect_channel Месяц назад

X=2 8×2=16 16=2^(2×2) 16=2⁴ 16=16

@claudelebourlegat 9 месяцев назад

and the other value ? ~ 0.155

@nitingl4730 9 месяцев назад

0.155 is another root, but this can be found out by Desmos graph. How to Know this other root as 0.155 ? Do you know how to arrive at 0.155 without using graph ?

@claudelebourlegat 9 месяцев назад

@@nitingl4730 Lambert function

@claudelebourlegat 6 месяцев назад

Only the Lambert W function(wolfram alpha)

@JacekWroński-u2z 8 месяцев назад

For a value of x equal to 2, we have a solution, but it is not the solution based on Lambert's W function presented here. For the given argument, the value of x equals 0.1550, which is confirmed by implementations in MATLAB, Python. How did you get the value of 2 ?

@Nikos_Iosifidis 8 месяцев назад

See my comment

@woncolee8848 4 месяца назад

直接心算2

@sergioweinberger562 7 месяцев назад

La ecuación tiene dos soluciones, como han dicho varios: 2 y 0.15495 (aprox). Las resoluciones gráficas con posterior aproximación de raices es aquí muy apropiado. Y evita el uso erróneo de transformaciones, funciones y complejos programas que no siempre se saben manejar.. Un estudio básico de la función 2^2x-8x (o directamente grafico con geogebra o cualquier programa) ubica los intervalos de sus raices, que son las de la ecuación. Luego de hacer esto si no me convencí que hay dos raices.... Lo último, no le veo aporte ninguno a la función de Lambert. Alguno llega a creer que sólo con ella se puede resolver esta ecuación.

@samuelMoses-q9n 9 месяцев назад

if a√5 + b√2 is the square root of 95 - 30√10, the values of "a" and "b" are respectively __ Pls someone solve

@felipe-n9t 7 месяцев назад

If you have two variables but only one equation, you can set the value of a to anything you like and then solve for b. There are infinitely many solutions.

@brunobuzzacchi1108 9 месяцев назад

Using Wolfram software I didn't get "2" for x, but 0.155...

@hansvangiessen8395 8 месяцев назад

There are 2 solutions: x=2 and x=0.155...

@danielfranca1939 9 месяцев назад

👍👍👍

@opulence3222 9 месяцев назад

Great video

@nitingl4730 9 месяцев назад

Can this equation be solved taking logarithm on both sides ?

@petrochengula9480 9 месяцев назад

Not at all

@hansvangiessen8395 8 месяцев назад

Try and see what happens... No succes. @@petrochengula9480

@AzharLatif-d4z 9 месяцев назад

Every Video falls short of evaluating the Lambert W Function because no one has tabulated the numerical values of this mysterious, useless Lambert W function, Don't waste your time on this bit of trickery.