One thing that I did not hear you explain is that the Lambert W function has countably infinite many branches in the complex numbers, so there are many complex solutions. You gave only one of them. Another is approximately 0.06396 - 1.0908i, yet another is 1.2484 - 5.5045i, and so on.

@onradioactivewaves

2 күн бұрын

...and so 4ᵗʰ.

The graphs of the functions y=x and y=4^x do not intersect.

Is there a reason why you keep saying 'natural log natural log 4'. It's just supposed to be said once, unless you're applying the function twice...

Somehow I do not feel enlightened

You have explained an answer that does not exist. You have not explained how you found the complex solution.

Es gibt keine reelle Lösung. Das wird durch eine Kurvendiskussion von f(x) = 4^x - x deutlich.

Stop the over explanation. This should not take 10 mins

Please can anyone explain me Lambert W function It is not in my course but still i want to know about it 😸

@justabunga1

3 күн бұрын

Lambert W function is the inverse function of y=xe^x and is a nonelementary function since it cannot be expressed in terms of x. Here, we denote the function notation as y=W(x). This means W(xe^x)=x.

@thenationalist8845

3 күн бұрын

@@justabunga1 thank you Is it defined for all Real numbers?

@rorydaulton6858

2 күн бұрын

@@thenationalist8845 If you are talking about the real-valued W function over the real numbers, no. W(x) is defined uniquely for all non-negative values of x, as well as at x=-1/e (where W(x) is -1). There are two branches of W for -1/e < x < 0. W(x) is undefined for x < -1/e. If you are talking about W(x) allowed to have complex values then W(x) is defined for all complex values of x.