Thanks but how to get the value of X in the calculator 🙏🙏🙏

X=0.309 (positive)

Thanks a lot.

Beautiful ! x^2+8 lnx = x^2+4 lnx^2. X=x^2. X + 4 lnX = 0. More easy ! Same result of course. Have a nice day !

Impossible to see the calculation on that board

One of the best video sis

Fantastic idea sis.

Please use one method in a video and make another video for second method to keep the length of video short, Thanks a lot❤❤

Nice explanation ❤❤

Thanks Sis for this function

Thanks Sis for this lecture

W is just an approximation like log. Nothing special about it. Now it is better if you use a computer numerically solving such equations, you do it at the end anyway by calculating W.

Great explanation

Also known as the KZbin Function.

Good pedagogy. Thanks

Thank you! I watched both videos and finally understand how this works!!

You could also simplify the answer to -2ln(2) / W(-2ln(2)) and/or change -2ln(2) to -2ln(±2), which can give you both the solution in the video and -2, which is also correct.

Can we evaluate W(y) if y = 1/x • e^x?

👍 💯 😀 " ≈ 2.207 - [Irrational part] " I expect you meant " ≈ 2.207 - [Imaginary part] " - ― £ $ € ฿ ± Σ Ω Π Δ µ ← ↑ → ↓ ^ √ ³√ ∞ * ≈ ≠ ≤ ≥ ÷ •

Thank you!

It's not a real solution

i love your explanation 🤗♥

There is no real solution. The x^2 and 8^x curves are within 0.37 at x=-0.6, but do not crross.

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?

thanks alot it really help me

Yes, it was interesting. Unfortunately, in university, I never had this problem. Backt then I loved math but not physics. I still love math and find physics much more interesting

I think there’s a rule for a^b vs b^a. If both a and b are larger then e, then the larger one is where the exponent is larger. Maybe it has a name?

Very good 👍

Very good. Please continue uploading similar videos 🙏🙏🙏🙏🙏

Very good. Thanks 🙏

so why does x not have 5 roots?/solutions if it is x^5?

Just an suggestion, when you did take the root you should explained why we do not take into account the negative part. I say this because some other problems will have both solutions, this is not the case but that need to be clear for us to understand...

This is not quite the correct use of the Lambert W function because it is multivalued. There are no real solutions because: -ln(8)/5 ≈ -0.416 < -1/e ≈ -0.368  Real number solutions are only if the parameter is above or equal -1/e. If the parameter is y, there are precisely two real solutions if -1/e ≤ y < 0, and only one real solution if y >= 0. (If there are two real solutions, the branch is always 0 and -1.) If you show complex solutions, you should mention that the Lambert W function always has infinitely many complex solutions, not just one. To get other solutions, you simply add the first optional parameter of the productlog function in WophramAlpha as any integer you like (the parameter is called branch).

Dear Intellecta, Your explanation of the solutions is very good. We understand the problems easily. My question in this problem is: W(-ln2 /10 ) has two answers. The first one is -4.073634 and the second one is -0.07469. However, you determined the result of the problem as x=0.107 by using the second one (- 0.07469) in solving the problem. Could you please explain, how can we understand this?

Dear Intellecta, Your explanation of the solutions is very good. We understand the problems easily. My question in this problem is: W(-ln2 /10 ) has two answers. The first one is -4.073634 and the second one is -0.07469. However, you determined the result of the problem as x=0.107 by using the second one (- 0.07469) in solving the problem. Could you please explain, how can we understand this?

Very nice example👍

Please use good chalk on the board

This was the best nap I've ever had :)

Very nice. Thanks!

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.

Why are you using the colon instead of Division? Is it some kind of culture? I'm korean.

As a result of the solution of this problem: When we look at the Wolfram table, which of the values W(-1/3 ) = -1.512135 and -0.619061 will we accept as the solution to our problem? You got the value - 0.619061. From where ? I couldn't understand this. Also, can you give me information about the application (used on phones or computers) where I can obtain the Wolfram table, which is the most used in solving such problems. Thank you. I wish you successful work. Kind regards.

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I love you 💕

Very good teaching 💯💯

Excellent explanation. Thanks 👍

Very good 👍

I believe it is not (1+sqrt(5))/4 but (1+sqrt(5))/2, isn't it?