How To Solve Exponential Equation x^5=9^x || Solving Exponential Equations.
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- เผยแพร่เมื่อ 1 ต.ค. 2024
- How to solve exponential equation of this kind is rhetorical but I will guide you on simple ways you can solve this kind of challenging exponential equations with easy.
In this video tutorial, I will explain to you on how to apply the Lambert W function to solving challenging exponential equations like this.
Watch from beginning to the end without skipping any parts for the full details.
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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.
2222232-81=
000000032
-49
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.
A complex solution is still a solution!!!
Hy.
This equation don't have real solution.
The graphic of f(x)=x^5-9^× is strictly negative. Tx
Bravo👍👍👍
You are the master here because you are good at what you do🙏🙏🙏
Respect👌👌👌
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
Am smoking maths hahaha...🤣🤣😂
@@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).
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.
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.
- ln9/5 is greater than --1/e because the interval semi close interval.. So, -- 1/ e is real. Negative number is real, not imaginary.
-0.881024 + 0.59038 i. Is the approximate answer to the Lambert W function.
@@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 < -1/e
-(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.
Oh but you see, there actually are multiple branches of the lambert function, spanning the entire complex plane and real line :>
Oh but you see, there actually are multiple branches of the lambert function, spanning the entire complex plane and real line :>
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.
Я нарисовал график в geogebra и там эти функции не пересекаются😮
I can prove that x^5
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.
@averycleverman But fewer people would watch a video called "I cannot solve an equation that has no solutions."
Well it has no real solutions but It actually 5 imaginary solutions and this is one of them
Aproksimativno resenje je kompleksan broj x=2.004857+i×1.584805
I am a math student(pursuing under graduate degree in India) from india and i just watched your video by TH-cam 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🎉❤
asnwer=3 isit hmm no math matter like isit 😂🤣😆😅
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 < 0, with the maximum of about -0.34 occurring near x = -0.6, i.e. there is no real solution to f(x) = 0.
Am I wrong?
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.
You have not yet checked whether your solution is correct or not
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 attempted another solution using the same reasoning:
define W: W^5 = 9^W. x=W QED
Find the answer.not in Lambert function.
Was für ein Geschmiere ....numerical value now ?
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?
But the image of 9^x does not intersect with the image of x^5
x is a complex number; see Demetrius above !
See answer of Ratko Dinic.
function W(x) defined on [-1/e; +00). So there is no solution, you need a mathematical object to reason.
I got that the risult is approximatively 0,34+0,23i 😞 what does that means? That the solution is irrational?
There is no real number x that satisfies this equation.
Real spill
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.
x = e^(2ln3/5) in the real plane
@@pureffm But there is no intersection point between x = ye^(y) and x = (-2ln(3)/5)
There is no w(-ln(9)/5) so the equation has no solution. Your explanation is wrong, wrong....
If you introduce a new function it doesn't make any sense. Lets define W(x) such that x=W(x)^5-9^W(x) and we get the solution x=W(0). That's not a solution...
Does the answer approve x^5= 9^× ?
Try to solve it by simple logarithm
You'll get 1.05 as answer viz Correct
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
So, what's is the numerical value of x that you sought now?
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.
But won't it have multiple solutions? As the input is negative?
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!
Dont have the answers. It usually isnt perfectly balanced in reason and equality of good and bad.
Hi sir
Please I need to understand as to how you immediately introduced logs on this without first tackling in normal way as others in this class.
the solution doesn't exist. You do not need a Lambert function to proove this. In case you do then at leat point out the the calculated Lambert value does not exist since it is
负数不能取对数吧
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.
Compute the Integral x^2024/(x^2+1)^2023 dx please.
Không có w(-ln(9)/5) nên phương trình vô nghiệm.
There is no real solution. Both curves never intersect. 9^x is always greater than x^5.
.x=3
X=9
Write down Powers of nine - 9,81,729.... Then write down powers of 3 - 3,9,27,81,243,729. The number 729 is common. So x=3. One solution is obvious.
What are you smoking?
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!
Lambert function😮 is new for me.
yea for me too
Professor, what does W mean in solving multiple equations?
Lambert function
답이 없는 문제임.엉터리 해법
@@조광일-h5i 본인이 모르면 답이 없는 것인가요? lambert function이라고 위에 답을 주었는데도 인터넷도 한 번 안 찾아보고 엉터리라고 말하다니..같은 한국인인 제가 부끄럽네요.
@@조광일-h5i학무위키라도 읽어라
@@태권정-z8yㅋㅋㅋㅋ 바보야
But which exam contains like this type of questions please tell me because I want to know?,
BUT YOU DID NOT FIND THE VALUE OF X....I TRIED AND FOUND OUT IT IS 3....MAKE THE RESPLCMENT AND YOU GET : 729=729....
Does the equation have a solution?
Sorry, but there is no solution. The function 9^x-x^5 is always greater zero, there is no solution for 9^x = x^5. You should better calculate by yourself and not copy other videos, where people made the same mistake.
Hahahaha.... you check out this same math problem if you see it on another math channels before the date I published mine, then bring it to my awareness and I will take down this video tutorial and apologize to you publicly sir.
Thanks in advance.
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
One of the solution of x
x≈-2.2756
love from sri lanka....😍
Thanks a million sir
I asked Chatgpt, and the answer is 2.478.
After a while of calculation, the author did not know that the equation had no solution.
Спасибо, профессор, Вы великолепны!
Even magicians fingers don't fluff about as much! All that to arrive at an answer that is more difficult to crack than the initial problem. What's the point of all that?
Well you can actually approximate the Lambert W function with an algorithm, but the answer shown in the video is the exact answer though, no approximation
Thanks for the keen observation sir. Your point here, is clear to us. OnlineMathsTV will appreciate it if and only if you can drop a clearer, simplier and more detailed approach with regards to this challenge sir.
We are here to equally learn from the best brains all around the globe too.
Much love💕💕💕
Thanks for the reply to this comment on behalf of Onlinemathstv sir.
Much love💕💕💕
The point of this is purely knowing that such manipulations are possible, and when you have a physics or other world application problem, because you are quite a smart creative person, you know that once you make an equation, you can shuffle numbers around, provided you don’t violate math rules, you could arrive at results you never could have thought of.
I say, I fear my head ooo
solving an equation by introducing a mystical new "function", for which everything is assumed to be known, does not solve the equation
Elaborate? It clearly did solve the equation
Nonsense. There is no real solution. The presenter probably meant to discuss x^6=9^x....
Oops!!!
X=3 is not a soluțion ?
You are on point sir, 3 is not one of the roots
What is the numerical value of W(-ln9/5? Which is the exponent of e?
x = e^(2ln3/5) in the real plane
The domain of the Lambert_W function in R is all z s.t z >= -1/e but -ln(9)/5 < -1/e, therefore -ln(9)/5 is not a solution and the ‘equation’ has no solution. Graph x^5 and 9^x in Desmos ad you will see that they do not intersect.
im really confused about this function , i saw that its defined on [-1/e,+oo[ so yhere is no solution , but my calculator shows there are two solutions, one of them is ~ -0.72 , and the other is complex
@@SCOrganisation Graph the two curves in Desmos. They do not intersect.
@@padraiggluck2980 i know , i discovered that calculater makes mistakes here , -0.7 is not true at all , cuz (-0.7)⁵= -(9-⁰'⁷) ≠ 9-⁰'⁷ , but the complex solution is true , they actually do not intersect in real plane
@@SCOrganisationx=-0.72 can't be a solution, for x^50. I wouldn't trust that calculator.... The complex solution might be (approximately) correct, however.
@@WK-5775 yes, when i tried to put x=-0.72 the two numbers were identical but in different signs, i use a calculator app and it is very strong, but i think it is an error in the app that it does not take the sign into account in complex (no relation to the complex numbers 😅) equations, but the other solution is correct 😁
Negative numbers has no logarithm!
9 and 5 must be switched in order to solve the equation
😂 just try out 3 ....
The answer is 3, you don't need this big calculations
Hahahaha😂😂🤣🤣🤣😂😂....my good friend you tried but that is not the answer sir.
Nice
🎉🎉🎉🎉
Когда делят на 5х , надо указать , что 5х/= 0 . А как писать не равен нулю .
It looks like you are invoking the Lambert W function without checking whether the argument falls within its domain. Unfortunately, it's not in the domain.
It falls in, check properly sir.
这个题在实数域上是不可解的，这个老师好像在用高科技玩泥巴
Bạn giải nhầm nghiệm. Coi lại lời giải
Great! But inconclusive.
I didn't understand anything you said
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
Incredible professor, thanks
You are most welcome sir.
And thank you for thanking us and appreciating our little effort sir.
We all here love you ❤️❤️💕💕💖💖
I didn't get past the 2nd line, you're good Sir, very good.
I don't know why the derivitive methode don't give the solution
ln(x)=(ln(9)/5)*x
(ln(x))'=((ln(9)/5)*x)'
1/x=ln(9)/5
x=1/ln(9)/5
You miss fired @step2 of your procedure. Take a careful division after taking the natural log and make all x terms to be on the LHS before differentiating. After that boom! you are good to go with this approach.
So what's the answer? Cmon man that's bs
Nice solution
This equation cannot have a solution in real numbers.
You can compare graphs, and they never intersect. This means that the equation x^5=9^x does not have a real number solution
Without solution😂😂
plug that into the Wolfram Alpha cal to get numerical value.
Burada tənlik həll etmək əvəzinə qəliz bir proses alındı.
does x = e ^ -W(- ln9/5) valid?
Teacher what does mean w in this equation?
You are taking ln of both sides without proving x>0. This does not seem okay.
İf x0 if we want two sides to be equal
noted sir and thanks for the keen observation
@@cellat0001 Perfect logic. This argument should be part of your solution before taking 'ln' of both sides.
🇩🇿🇩🇿 شكرا
So this is where we landed ? Just like leaving Egypt and still faced with the Red Sea
🤣🤣🤣🤣😂😂😂🤣 you make me laf uncontrollably @Aloysiusdaniel.
You can get the numerical values from Wolfram Alpha calculator at this point sir.
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)
So what is X in numerical values?
Prof. Are u from Nigeria?
This is totally absurd, just substitute the solution by so called “w” function, means nothing
Very good
45
Please make more such videos on harder algebra.
Solusinya masih berupa rumus
😢
Hahahaha, just input that final answer you called formula into your Wolfram Alpha calculator and you will definitely get your correct answer when substituted into the original equation.
Thanks sir.
3
8>>>> too fast...!!!!
У меня единственный вопрос - почему негры в шахматы не играют?
3
I just thought for sec that can answer be 3 for x
No sir, kindly resolve sir.
대한민국 고등학생한텐 너무 우스운 문제..
대한민국 고등학생은 람베르트 W 함수를 알지 못합니다..
당장 미적분에서도 초월함수 방정식의 해는 구하지 못하는 경우가 태반입니다
Would you please make a video on Lambert Function, professor!?
Dear professor! What is ld function?
Answer 9