I am a math student(pursuing under graduate degree in India) from india and i just watched your video by KZread suggestion and I like you way to solving problem with explain in very eazy language and I like it thank you please made more videos like this for improving students mathematical knowledge. Thank you🎉❤

Nice 🎉🎉🎉🎉

Love the clever way to solve problem. However, the solution’s argument for the W Lambert function (-Ln (9)/5) is outside the domain of such function [-1/e, ∞). The curve X^5 - 9^x does not intersect the X axis, the closest value (y=-0.345) occurs when x=0.589.

@user-nz7kx1dn4n

5 ай бұрын

2222232-81= 000000032 -49

@slobodanjergic5257

5 ай бұрын

Rafael is absolutely right - given that (-ln(9/5) < -1/e, the conclusion of this exercise should have been to prove at the end that there are no real solutions to above given equation. In relation to that, It would have been useful to theoretically explain this outcome by sketching W(x) function and concentrating particularly on the meaning of the point -1/e in order to understand the concept behind the proof.

@oliveirafilipe5416

2 ай бұрын

A complex solution is still a solution!!!

Its first time I saw the lambert W Function, when I study Calculus I and II, my lecture never taught this Lambert W Functions. I'm very blinde about this them... Please make more video especially about this Lambert W Functions. For your respect, thanks very much.

Nice solution

The domain of the W function of a real number is [-1/e, ∞). The argument (-ln 9)/5 is less than -1/e. Consequently, W((-ln 9)/5) does not have a real number value. The two curves do not intersect in the real number plane, as can be confirmed by plotting them using the online graphing app Desmos.

@syedmdabid7191

8 ай бұрын

- ln9/5 is greater than --1/e because the interval semi close interval.. So, -- 1/ e is real. Negative number is real, not imaginary.

@SalmanAkhtar1

8 ай бұрын

-0.881024 + 0.59038 i. Is the approximate answer to the Lambert W function.

@user-qn1zn3uo2x

7 ай бұрын

@@syedmdabid7191 Product logarithm is multivalued function in real number. W0: [-1/e, ∞) -> Real number W1: [-1/e, ∞) -> Real number Dom W= [-1/e, ∞) 3 > e > 2.5 ln x ↗ ln 9 > ln (e²) = 2 >5/e (ln 9)/5 > 1/e -(ln 9)/5 -(ln 9)/5 ∉ [-1/e, ∞) W [-(ln 9)/5] ∉ Real number => The solution can only be in complex numbers; there is no solution in real numbers.

@ThatobjectArtist

5 ай бұрын

Oh but you see, there actually are multiple branches of the lambert function, spanning the entire complex plane and real line :>

@ThatobjectArtist

5 ай бұрын

Oh but you see, there actually are multiple branches of the lambert function, spanning the entire complex plane and real line :>

Спасибо, профессор, Вы великолепны!

Incrível!

Thank you very much, professor. This was the first time I saw the Lambert function used to solve an equation. This is amazing! And it's nice to learn new things!

Thank you professor

very good algebric problem

🎉well said sir

You really love math and teaching!!!

I first came accross this type of problem when I was trying to answer a question regarding compound interest vs simple interest : ax = b^x where "a" and "b" are known quantities.

I like wrapping my mind around these Olympiad problems. They are most cleverly put together. They're designed to make us think outside the box to come up with a simple, elegant approach to the problem at hand.

Lambert function😮 is new for me.

@theriaa4580

5 ай бұрын

yea for me too

Great Lambert function (W)

@onlineMathsTV

Жыл бұрын

Thanks for watching and commenting sir. Much love from all of us @onlinemathstv to you sir 💕💕💖💖🙏🙏.

Incredible professor, thanks

@onlineMathsTV

Жыл бұрын

You are most welcome sir. And thank you for thanking us and appreciating our little effort sir. We all here love you ❤️❤️💕💕💖💖

Very good

Great work.From India.

I never went to olympiad. but as sweet you solve this, I really enjoy and occuping with it. Many thanks dear bro!

i attempted another solution using the same reasoning: define W: W^5 = 9^W. x=W QED

Nice explanation professor thanks 🙏🙏🙏

Good one

Nice explanation sir

@onlineMathsTV

10 ай бұрын

Many thanks to you for the acknowledgement sir. Much love from everyone @OnlinemathsTV ❤️❤️😍😍💕💕💖

I only watched the video because I couldn't solve it and I realised that it probably has no solution because the graphs of Y = x^5 and y = 9^x do not intersect. I thought I will be impressed if he can solve it and tell us the solution but he didn't give us any solution at all, he simply played with symbols. He should have been honest from the beginning and said this actually has no solution.

@user-gd9vc3wq2h

8 ай бұрын

@averycleverman But fewer people would watch a video called "I cannot solve an equation that has no solutions."

love from sri lanka....😍

@onlineMathsTV

2 ай бұрын

Thanks a million sir

I didn't get past the 2nd line, you're good Sir, very good.

Brilliant work again thanks so much teacher

@onlineMathsTV

Жыл бұрын

Thanks for the encouragement sir. Much love

This is great approach master. I love this, and i have learnt some thing new sir. Thanks master 🎉🎉❤❤

@onlineMathsTV

6 ай бұрын

Happy to hear that!

Please make more such videos on harder algebra.

Hy. This equation don't have real solution. The graphic of f(x)=x^5-9^× is strictly negative. Tx

@onlineMathsTV

Жыл бұрын

Bravo👍👍👍 You are the master here because you are good at what you do🙏🙏🙏 Respect👌👌👌

I understood, THANKS A LOT

@onlineMathsTV

Жыл бұрын

You are welcome, and we are glad u gained some values from this video tutorial sir. Much love 💖💖💖

Aproksimativno resenje je kompleksan broj x=2.004857+i×1.584805

great approach but.....😍😍😍😍😍😍

@onlineMathsTV

11 ай бұрын

What's wrong with the content sir? We are very open to corrections and criticism.

Nice sir

We really appreciate it.

Just found that the general solution for "xᴬ = Bˣ" is: x = - W(ln ⁡b/a) / (ln ⁡b/a) Obviously I haven't really paid attention to W domain subjects.

I can prove that x^5

very good

@onlineMathsTV

5 ай бұрын

Thank you my good friend

Nice explanation and thanks for this video Jakes.

@onlineMathsTV

11 ай бұрын

Thanks for appreciating our little effort sir Much love from Onlinemathstv 💖💖💖💕💕💕

Thank you for the video!! Turn my maths fear and anxiety earn in the past 15 years from a teacher I had…to an opening in mathematics again

@onlineMathsTV

9 ай бұрын

Its a pleasure serving you in this regards and we are glad you gained some values from this video tutorial sir. We will do our best possible to serve you and others better in this endeavor. Maximum respect sir...🙋🙋

@MsOZ79

9 ай бұрын

Thank you Sir, your response is so overwhelming. Thank you

Я нарисовал график в geogebra и там эти функции не пересекаются😮

Nice video

@onlineMathsTV

9 ай бұрын

Thanks for watching and finding some values in our video sir. Much love master.

Спасибо учитель,я не понемаю твое слова,но понемаю твое решения задач,я блогадарень тебя,очень хочу с тобой обшатся,я из УЗБЕКИСТАНа,знешли ты такое государства

Great! Thanks for the rigorous approach! Greetings from Italy!👍👍👍👏👏👏👏

@onlineMathsTV

Жыл бұрын

You are most welcome sir, and thank you for watching our video tutorial and leaving a comment behind. We love 💖💖❤️❤️

@MdKamal-wt8xt

10 ай бұрын

Sir,please express of W

So, what's is the numerical value of x that you sought now?

it is simple

@onlineMathsTV

Жыл бұрын

Sure master, it shows you are the master here and you are good at what you do sir. Respect👍👍👍.

Very impressive usage for Lambert W function, but if you do not use a few more explanations about "Productlog function", I think many of your audiences will not eventually reach the final point.

It's interesting, that in according a formula e^nW (x) = [x/W(x)]^n: n = -1 and e^-1 W(-ln 9/5) = [(-ln 9/5)/W(-ln 9/5)]^-1 = W(-ln 9/5)/(-ln 9/5)

The first time I understand the Lambert functions

Would you please make a video on Lambert Function, professor!?

Interesting exercise, rigorous approach... Thanks ! Congrats ! Keep it up ! Good luck with your work !

@onlineMathsTV

Жыл бұрын

😍😍😍 Thanks so much for this wonderful comment you dropped here.

@zadabjlil2281

Жыл бұрын

​​@@onlineMathsTVut lambda ₩ 👍؟؟????🦧🦧

@johnback0007

11 ай бұрын

​@@onlineMathsTVs this college level math? If so what class is it? I never seen this in high school

Great work, sir it was vey hard challenge, bt any way thanks.

@onlineMathsTV

Жыл бұрын

Thank you for watching and appreciating our small effort so far. We love you sir❤️❤️💕💕

very nice approach

@onlineMathsTV

11 ай бұрын

Glad you liked it and thanks for watching and commenting sir. Much love 💖💖💕💕💕

🇩🇿🇩🇿 شكرا

Dear professor! What is ld function?

Compute the Integral x^2024/(x^2+1)^2023 dx please.

Great! But inconclusive.

I asked Chatgpt, and the answer is 2.478.

Какой приятный парень. Но я не понял решения в конце - что за функцию он ввел, когда приравнял А на Е в степени А к просто А? Чему же равен Х? Что за функция в решении?

asnwer=3 isit hmm no math matter like isit 😂🤣😆😅

This is the real solution and no doubt about it x = -(5 W_n(2/5 (-1)^(3/5) log(3)))/(2 log(3)), n element Z or

@OlarewajuAdebayo-mf7pm

6 ай бұрын

One of the solution of x x≈-2.2756

Well, when I first saw this I thought “there’s no way 9^x ever meets x^5 , right? Cause a power function is always above the x-axis…and there’s no way for any x^a (a>0) to catch it since such functions flatten out from 0 to 1…so…what is this guy smoking?” Perhaps I’m missing something? Like a good hit. :p 三八弟

@onlineMathsTV

6 ай бұрын

Am smoking maths hahaha...🤣🤣😂

@mr.9754

6 ай бұрын

@@onlineMathsTV Oh I see your solution must be an element of the Complex numbers...ok..haha...This is all new math for me, but I get it now. ps You can google "Wolfram Alpha" and then enter "productlog(A)" ...which is equal to W(A) pps Can I offer a little unsolicited advice? Let your audience know the domain of your x whenever you introduce a function. Also, point out that W(A) will only have real number solutions if A is greater than 1/(-e).

But how could you find the numerical value of W-n ( -- ln 9/5)??? For this, you must have to apply Newton Raphson method / graphic method.

@Anmol_Sinha

7 ай бұрын

But won't it have multiple solutions? As the input is negative?

@ashwinm6509

7 ай бұрын

I'm pretty sure there is no solution to this equation since if u plot the curve of x^5 and 9^x, they don't have any intersecting points!

Teacher what does mean w in this equation?

But which exam contains like this type of questions please tell me because I want to know?,

Try to solve it by simple logarithm You'll get 1.05 as answer viz Correct

Does the answer approve x^5= 9^× ?

The equation has no solution in the real domain. You can check that by plotting a graph. You can try to solve the equation in the complex domain, but then you have to be careful with the logarithms.

@pureffm

7 ай бұрын

x = e^(2ln3/5) in the real plane

@user-ih2du9nw3u

7 ай бұрын

@@pureffm But there is no intersection point between x = ye^(y) and x = (-2ln(3)/5)

Когда делят на 5х , надо указать , что 5х/= 0 . А как писать не равен нулю .

This great but I think this math is beyond my level. Anyway, thanks for dropping this nice video sir.

@onlineMathsTV

Жыл бұрын

You are most welcome

What is the numerical value of W(-ln9/5? Which is the exponent of e?

@pureffm

7 ай бұрын

x = e^(2ln3/5) in the real plane

It's beyond my ability to understand

I was going to say that... (who's Oliver?)

So what is x that solves the equation? Give us the value. Plotting f(x) = x^5 - 9^x I have satisfied myself that f(x) is always Am I wrong?

@wearron

10 ай бұрын

no, you are correct. There is no real solution. But, for some equation of the "n^x = x^n" sort, it is very useful to keep the W in mind. There are infinite solutions in the complex plane, meaning there is no single solution( because the lambert function takes in a number for its power, but in this case the number is absent, meaning it can be anything from the real plane.)for the equation, rather a set of infinite ones. there is a total of 5 formulas for solutions, hence 5 infinite sets of solutions(not counting the lamber power). I can give you one right now, approx. 7.92822 -31.61131 i, where i=√-1.

Find the answer.not in Lambert function.

负数不能取对数吧

So what is X in numerical values?

This is only one of the 5 solutions. Can you share the other 4 solutions? I listed all 5 solutions using log function below in the reply to my comment. If you can show the full solutions that will be helpful.

*Do not fear, the Lambert W function is here!*

so what is the value in decimal form? I want to substitute it to double check.

@onlineMathsTV

9 ай бұрын

You can get that from your Wolfram Alpha calculator sir.

@gerar2158

8 ай бұрын

La wolframalpha no da un valor numérico en es te caso

Base =9 Power : 5

3

After a while of calculation, the author did not know that the equation had no solution.

9 and 5 must be switched in order to solve the equation

Professor, what does W mean in solving multiple equations?

@onlineMathsTV

Жыл бұрын

Lambert function

@user-ur2sq7od5t

11 ай бұрын

답이 없는 문제임.엉터리 해법

@user-nb5qm7kv1o

10 ай бұрын

@@user-ur2sq7od5t 본인이 모르면 답이 없는 것인가요? lambert function이라고 위에 답을 주었는데도 인터넷도 한 번 안 찾아보고 엉터리라고 말하다니..같은 한국인인 제가 부끄럽네요.

@mr_rocketluckit5294

10 ай бұрын

​@@user-ur2sq7od5t학무위키라도 읽어라

@uggupuggu

10 ай бұрын

@@user-nb5qm7kv1oㅋㅋㅋㅋ 바보야

Hi❤❤❤

БОЛГАРИЯ АЛФА

but what is the value of λ？

The Lambert function of a negative value (-log(9)/5 < 0 always) will result a not real value. So, there is no x € |R that satisfy x⁵ = 9^x.

45

But the image of 9^x does not intersect with the image of x^5

@ulrichkaiser3794

11 ай бұрын

x is a complex number; see Demetrius above !

@user-kg8qv7ri6z

7 ай бұрын

See answer of Ratko Dinic.

Prof. Are u from Nigeria?

So this is where we landed ? Just like leaving Egypt and still faced with the Red Sea

@onlineMathsTV

Жыл бұрын

🤣🤣🤣🤣😂😂😂🤣 you make me laf uncontrollably @Aloysiusdaniel. You can get the numerical values from Wolfram Alpha calculator at this point sir.

The graph of the two functions (x^5 and 9^x) never ever intersect each other, that means there is no solution, I already tried to solve it by numerical methods , No solution

I got that the risult is approximatively 0,34+0,23i 😞 what does that means? That the solution is irrational?

Answer 9

.x=3

@natarajan.g.v6236

10 ай бұрын

X=9

I think a better problem would have been x^5=5^x. It has a pleasant symmetry and perhaps more importantly, a real solution. I am pretty sure that the actual problem in the video has only imaginary solutions.

@onlineMathsTV

6 ай бұрын

Only imaginary roots