A beautiful math question for advanced students

What do you think about this problem? If you're reading this ❤️.

Hello My Friend ! Welcome to my channel. I really appreciate it!
@higher_mathematics

#maths #math

[gamertz]

Beside the math did anyone try to remove hair from screen like me in beginning?😂😂🤣

[justliberty]

I'm 63. I have a PhD in engineering. I've never heard of Lambert's W function.

[Akenfelds]

This video labours dead simple mathematic steps like it was high school mathematics, but offers no explanation of Lambert's W function. It's like watching somebody make a ham and cheese sandwich with a step-by-step guide as to how to slice ham but no explanation as to where bread or cheese comes from.

[StatisticalLearner]

Well, beauty is in the eyes of beholder. So there is no sense of arguing whether this solution is beautiful or elegant. It however, borrows something itself is quite esoteric and difficult to understand, vis a vie, the Lambert W functions, to seemingly solve another enigmatic equation. Except it actually does not solve it in the close form (that can be expressed with elementary equations), because Lambert W function can only be solved numerically. If that is the case, it is much easier to solve the original equation numerically. In addition, the solution in this video actually mis represented the value of Lambert W function. It is a function that has many (complex) branches leading to many roots, and the true beauty is in how these branches, and roots are related to each other. For those looking for beauty in mathematics, you are more likely finding it in the Lambert W function itself. It is also worth noting, the Lambert W function is actually fully developed by Euler, and it has an important place in Dirac's quantum mechanical representation of chemical bonds and other important physical phenomena. And the fact that Euler developed the function and derived its properties a couple hundred of years before its application in science is mind-blowingly beautiful.

[rorydaulton]

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.

[PNLMaths]

I am a four year trained Maths teacher with a pure Maths degree and 35 year experience of teaching all levels from year 8 to year 12. From the graphs of y = x and y = 4 to the power of x, we can easily see that they have no intersection. That's enough to conclude the above equation has no real solution.
That's it.
What is Lambert function?
Thanks.

[tuho]

No need to complicate the problem. From the equation x cannot be negative. With x>=0, taking ln of both sides and using the upper bound of a natural logarithm, we can easily prove that x*ln4 > lnx so there’s no solution.

[PavelKucera-bddd]

Sorry, but Thus 4^x≠x. Your root is not a solution of the equation.
The first root of this equation is 1.248-5.505i since

[davidchilds]

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

[zdrastvutye]

this time it will work also for a=1.1 or a=2 or a=4, see line 10:
10 a=4:print "higher mathematics-a beautiful math question"
20 sw=.1:b=sw:goto 50
30 csc=b/a^b:if csc>1 then stop
40
50 gosub 30
60 b1=b:dg1=dg:b=b+sw:if b>100 then stop
70 b2=b:gosub 30:if dg1*dg>0 then 60
80 b=(b1+b2)/2:gosub 30:if dg1*dg>0 then b1=b else b2=b
90 if abs(dg)>1E-10 then 80
100 print b, c
110 print or"
120 print
higher mathematics-a beautiful math question
0.250501609 1.39285046
or

>
run in bbc basic sdl and hit ctrl tab to copy from the results
window. if there is a mistake, let me know. see also wolframalpha

[winstongludovatz]

This is painful, the most trivial inequalities will show that there is no real solution. Higher mathematics?

[LelekKozodoj]

You made a mistake. -0.0887+1.5122i is a value of W(-ln(4)), and not 1/exp(W(-ln(4)). Therefore it's not a value of 'x'.
The solution is x = 1/exp(-0.0887+1.5122i).

[papkenhartunian]

Could you explain how you found the complex root?

[ajitandyokothakur]

You keep repeating "Natural log Natural log..."). It is probably your verbose but some might find it confusing. Dr. Ajit Thakur (USA).

[Anti-You]

I was an applied math major and I've taken complex analysis. I've never heard of the Lambert W function. Wolfram classifies it as "Miscellaneous Special Functions" and it seems that it has this one useful quality. It'd be good if you'd have an example that doesn't result in an imaginary answer. I'd like to see it.

[luckyluk]

you found a complexe root using a complexe way😅 ! there a simple way just from line 4 . you plot the function ln (x)/x - ln4 = 0. you ´ll find the graph below and not touching the x axis, which means no real roots .

[mdrokebtamim]

This question itself wrong. How it is possible to X is more bigger than X 😂😂😂.

X=4^x impossible.

[nooruddinbaqual]

Lambert W function is confusing
Is it of any practical use or serves as brain teaser only?

[xypherdrakeinsignia]

You can hav 4 as 2^2(x) = x^1
The solution of the x power can be solved = 1/2
Substitute the x power to 1/2 for 4 or square root of 4 is 2 hence the variable x is equivalent to 2

[skateordiee]

Wait, I think I figured it out… X = X lmao 😂