there is something called “mathematical induction” it is legit
@張三豐-l4v
2 ай бұрын
這確實不是好的解答
@timmy18135
3 ай бұрын
Just use logarithm
@progr6171
3 ай бұрын
Geterosexual logarithm*
@saturninufolud6767
3 ай бұрын
You would receive something with the Lambert W function (irrational in general)
@progr6171
3 ай бұрын
mу соmmеnt wаs dеlеtеd.... It sаid: hеtеrоsехuаl lоgаrithm
@gmddlex5873
3 ай бұрын
@@progr6171спалился
@AW-dt8ct
3 ай бұрын
@@progr6171 And is there the homosexual one?
@oguzkk
Ай бұрын
Solution set of This equation has three real roots. One of them is 256. in the question, it has to be stated that x was an integer.
@jamesmarshall7756
4 ай бұрын
I use the Lambert W function to resolve x^32=2^x. «ln» both sides : 32 lnx= x ln2. So lnx/x = ln2/32 the same as (x^-1) lnx = ln2/32. x^-1 = e(ln(x^-1)) and lnx = -ln(x^-1). So we have : e(lnx^-1) x ln(x^-1)= -ln2/32. So lnx^-1 = W(-ln2/32). «e» both sides : x = 1/(e(W(-ln2/32))
@K.Klogic
4 ай бұрын
Thank u for your solution ❤️💕💖
@77das
3 ай бұрын
Сложно назвать это математическим методом решения, скорее простой подбор.
@elmanmusaiev7003
3 ай бұрын
Это не совсем подбор. Методология и тактика тут есть. Подбор был сделан под конец, что подпортило эффект. Подбора можно было и не делать. Но понадобилась бы вычислит машина. И снова была б критика ))
@ArinaAnn
3 ай бұрын
@@elmanmusaiev7003 зачем машина, выше правильно про логарифмы написали. А показаний способ это все же подбор.
@leviansilva1102
2 ай бұрын
A matemática é um jogo fascinante!!! Gostei.
@K.Klogic
2 ай бұрын
Thank u for your comment ❤️
@aleksandrajones4101
3 ай бұрын
So what about x=1.022 and x=-0.979?
@luzak2k
3 ай бұрын
Error
@daniel-mircea
Ай бұрын
these are the other two real solution of the equation.
@kusumikasiddhanta607
2 ай бұрын
Using logarithmic fuction is the true solution for this particular sum...because it is not a solution unless you are able to solve all the similar types of sums using that method, irrespective of the base and the exponent...for example if it was 31 instead of 32...using this method would have fetched us nothing at all.
@Observer1973
3 ай бұрын
You have lost two additional roots.
@SameerMalik-ur8gb
6 күн бұрын
When u know the answer and try to get it anyhow 😂😂
@soshakobyan3123
2 ай бұрын
This is guess and check method, so you must prove there are no other solutions.
@alexeyevgenevich9821
4 ай бұрын
2^256 = 1,1579*10^(77)
@ИванСафронов-ж9с
3 ай бұрын
А разве данное уравнение имеет не 3 решения? Автор указал всего 1, но их 3
@EliabBezerrademello
3 ай бұрын
I DONT UNSESTAND THE FINAL
@СергейПопов-э9о
4 ай бұрын
Thanks for the video. Maybe someone knows how to find these two more solutions for this problem? (~ -0.979 and 1.0225)
@K.Klogic
4 ай бұрын
Thank you for your comment ❤️
@screemer949
3 ай бұрын
Yes, I published actual solution in comments
@АлексейЯкушин-щ4й
4 ай бұрын
But you don't proof that is only one solution. In naturals, yes, one 256, but in reals is one more root at interval [1,2]
@anton-ke4qz
4 ай бұрын
But Why we don’t do any not equivalent transformation? Or do? To loose another solution in real numbers? Or there is negative solutions have been lost?
@АлексейЯкушин-щ4й
4 ай бұрын
@@anton-ke4qzThis solution is not correct
@jeanpierre7971
4 ай бұрын
Don't you need to prove that x -> x^(1/x) is bijective?
@Drestanto
4 ай бұрын
not really as long as you do the verification at the end
@jeanpierre7971
4 ай бұрын
@@Drestanto Then what guarantees that there is no other solution?
@Drestanto
4 ай бұрын
@@jeanpierre7971 yes, there's no guarantee for a unique solution If it's bijective, it has a unique sol What I meant is that x -> x^(1/x) does not need to be bijective to make one solution works as long as there is a verification at the end
@jakefromstatefarm6969
4 ай бұрын
Given that this is a competition question posed to us, there is no need to prove anything. All that is needed is determining a solution, not proving that it is a unique solution.
@pedjolinko
4 ай бұрын
@@jakefromstatefarm6969 You are very wrong. First of all, there are two solutions though only one is an integer.
@yatingkang3257
3 ай бұрын
x is also approximately equal to 1.0223929402058
@stevenschmidt
4 ай бұрын
256 isn't the only solution.
@K.Klogic
4 ай бұрын
Dear sir u can solve ❤️💖💕
@mcrow312166
4 ай бұрын
I love the way you communicate without words.
@K.Klogic
4 ай бұрын
Thank you for your comment ❤️
@davidbrown8763
4 ай бұрын
...and with decent music, unlike so many other channels. I have just liked and subscribed.
@K.Klogic
4 ай бұрын
@@davidbrown8763 thank you dear sir.supor my channel thank u💖❤️🎉
@davidbrown8763
4 ай бұрын
@@K.Klogic I am a supporter.
@K.Klogic
4 ай бұрын
@@davidbrown8763 thank you dear..
@Hasanhuseyinyilmazofficial
Ай бұрын
Logaritma kullancak misin diye merak ettim tum videoyu izlemek zorunda kaldim😑
@babysharddooloolooloo
Ай бұрын
There are three answers...
@K.Klogic
Ай бұрын
Exactly
@КатяРыбакова-ш2д
3 ай бұрын
x=256
@iwanagustinusong3506
Ай бұрын
X = 0
@IoanaSandu-i8z
3 ай бұрын
Nu este o rezolvare coerenta. Nu m- ai convins
@曾恩量子力學
3 ай бұрын
naturelogrithium "ln"
@K.Klogic
3 ай бұрын
Thank you for your comment ❤️💖
@ouldmedouldmedmr9489
3 ай бұрын
Is n'nt anallytique nor mathamatical
@glitch9643
3 ай бұрын
Cant we use log here?
@K.Klogic
3 ай бұрын
Try first
@Cetin0707
Ай бұрын
No sense
@sucremanswhite3951
2 ай бұрын
Totally wrong...
@K.Klogic
2 ай бұрын
No problem ❤️
@심심타파-t6p
3 ай бұрын
1
@K.Klogic
3 ай бұрын
Thank you so much for ur comment
@howardhavlicsek5031
4 ай бұрын
Doesn't look like anyone is willing to solve the problem, just guess at a solution! What if the problem was 2^x = x^31?
@dhy5342
4 ай бұрын
Then X would equal 1.0231407...
@K.Klogic
4 ай бұрын
Thank you for your comment ❤️
@K.Klogic
4 ай бұрын
Thank you for your comment ❤️💖
@MKPoqdPDeamimzpygxDjg7sJY59
3 ай бұрын
@@dhy5342 or about 246.266
@jursamaj
3 ай бұрын
@@dhy5342 Also 246.266…, plus 5 families of complex answers.
@vvv1041
3 ай бұрын
This method isn’t analytical. For instance, it doesn’t answer if this equation has only one solution. For the similar equations like that but with different coefficients it will not work.
@K.Klogic
3 ай бұрын
Thank you for your comment ❤️💖
@jursamaj
3 ай бұрын
Indeed, there are 2 other real solutions, plus multiple families of complex solutions.
@sergeykardash4482
3 ай бұрын
@@jursamaj1 more real...
@zorg6020
2 ай бұрын
Есть и проще решение чем то что в видео. Найти решение на пересечении графиков функций. Вот и все.
@cristinap.7498
Ай бұрын
A me basterebbe trovarne una
@busraakagunduz.
Ай бұрын
Soruyu gereksiz uzatmış. Her iki tarafın logaritmasını alsa zaten sonuç çıkardı
@pub7496
4 ай бұрын
Thanks for the interesting problem. I liked the way you present. Subscribing
@K.Klogic
4 ай бұрын
Thank u dear sir❤️💖
@markharder3676
4 ай бұрын
Take a guess and assume that like 32, the answer is a power of two. Use logarithms in base 2 because log(2, 2^x) = x. and log(2, x^32) = 32 log(2, x). Or, x = 32 log(2, x). So x / log(2,x) = 32. This can be solved by inspection, again beginning with powers of 2: x is divided by x as some power of 2, Trying a few values of x we see that log(2,256) = 8 and 256/8 = 32.
@K.Klogic
4 ай бұрын
Thank you for your comment ❤️💖
@rickkwitkoski1976
4 ай бұрын
@markharder3676 Thank you.
@diwakaranvalangaimanmani3777
4 ай бұрын
This method for people who don’t know logarithm
@b213videoz
4 ай бұрын
Very convoluted
@antoniopetrolagarrigos9771
3 ай бұрын
@@diwakaranvalangaimanmani3777if you know exponents you have to know logaritms😂
@YasinBEY-eo1ng
3 ай бұрын
Şöyle bi bakayım dedim denerken buldumn😅256 deneme yanılma cikiyor
@manassarma735
2 ай бұрын
I must be super drunk off my ass to have watched the whole thing
@chrisj5443
4 ай бұрын
A couple minutes of trial and error yielded x=1.0225 or thereabouts.
@K.Klogic
4 ай бұрын
Thank you for your comment ❤️
@Sci-Marvels
18 күн бұрын
Nice work! Sometimes a bit of trial and error can quickly lead you to a close approximation
@Lincoln-ht2dv
3 ай бұрын
Too many steps. Waste of time.
@radutrimbitas4930
3 ай бұрын
there are 2 more solutions, x\approx -1.022 x\approx -0.979
@hkleiser5848
3 ай бұрын
i think you should show that the problem has only one solution to get all points, without that solution isn't full
@JSSTyger
3 ай бұрын
It looks to me as if there must be a solution between x=1 and x=2
@K.Klogic
3 ай бұрын
Ok
@rubixpuzzlechamp
3 ай бұрын
@@K.Klogicand a negative solution. There are 3 real solutions.
@Swamisonic18
3 ай бұрын
How to find all solutions? Tell the method please🙏@@rubixpuzzlechamp
@ardalex4277
2 ай бұрын
The answer is not complete. I guess there is another solution in (-1,0) interval. And another one in (1, 2) interval.
@K.Klogic
2 ай бұрын
Yes dear i mention already
@loanct
3 ай бұрын
this problem have 3 answer
@sarvarmahmudov6276
23 күн бұрын
X=32 can be a root too
@WiXGaminG
2 ай бұрын
Your mind has to work in a strange way to be able to comprehend such things :D to me its pure magic😂
@ЛарисаРашевская-э3щ
3 ай бұрын
Если условие найти натуральный корень, то решение класс, если количество корней, то по графику видно два и третий, который 256, его надо догадаться, за интересное уравнение спасибо!
@K.Klogic
3 ай бұрын
Thanks 💕
@Sci-Marvels
18 күн бұрын
Согласен, если условие - найти натуральный корень, то решение отлично подходит. Но по графику действительно видно два корня, а третий, который равен 256, нужно догадаться. Спасибо за интересное замечание и внимание к уравнению!
@elenaokon2736
2 ай бұрын
Curves 2^x and x^32 intersect twice: x at one intersection is positive, and at the second intersection is negative. So there should be two solutions.
@K.Klogic
2 ай бұрын
Good dear ❤️
@KarlHandke
Ай бұрын
This world is not normal.
@ЭдПетр
4 ай бұрын
-0.979 approximately next solution. There are three solutions
@K.Klogic
3 ай бұрын
Thank you for your comment ❤️💖
@tahamuhammad5962
2 ай бұрын
TZZ {4,2,1} Tzz is the Taha + Collatz brand. Factories of T-shirt, sports shoes, engineering machinery and tools, airplanes, cars, trains and ships must use this mighty sign that signifies victory and the solution of Collatz. So factories must agree with me to use this mark. Author: Taha M. Muhammad/ USA Kurd Iraq Bakuage Thank you prepare your prize
@erkincakar7966
Ай бұрын
2 base 4=4 base 2 32×4=128×2=256
@servetoksuz7153
11 күн бұрын
Just say x=2^a, than solve for a. That would br a lot faster.
@K.Klogic
10 күн бұрын
👍
@jojojo7333
10 күн бұрын
Now solve 4.67^x=X^23.4
@Yacine-e9p
Ай бұрын
Suite de fonction ; introduction à la série de Fourier
@Limited_Light
4 ай бұрын
It may be worth noting that 2 divides 2^x if x is natural number, so 2 would have to divide the right hand side as well. I think it's Euclid's Lemma that would then tell us x has to be at least a multiple of 2, if not a power of 2.
@K.Klogic
4 ай бұрын
Thank you for your comment ❤️
@Sci-Marvels
18 күн бұрын
Great observation! Indeed, if x is a natural number, 2 divides 2^x, so the right-hand side must also be divisible by 2. Euclid's Lemma is a helpful tool here, suggesting that x should be at least a multiple of 2, or even a power of 2. Thanks for bringing this up!
@Limited_Light
18 күн бұрын
@@Sci-Marvels In hindsight, I wonder if there's a way to show x must be a *power* of 2. Overall, though, I think this and similar questions are related to the Lambert W Function, without getting into that.
@Sci-Marvels
17 күн бұрын
@@Limited_Light that's a great question! It would be interesting to explore if x must be a power of 2. You're right that this and similar questions often relate to the Lambert W Function, even if we don't delve into that here. Thanks for bringing this up!
@Tatarin374
3 ай бұрын
Бестолковые цифры. 99% никогда неиспользуют математику такую. Базовая нужна. А не вот такая порнушка
@K.Klogic
3 ай бұрын
Respect your comment ❤️
@pomupomu0624
2 ай бұрын
이게 올림피아드 문제냐 ㅋㅋㅋ 양변에 로그 취하라고 ㅋㅋㅋㅋㅋㅋ
@KORGUSUS
Ай бұрын
Answer x=8 i solwed five seconds.
@АнтонСергеев-ъ9н
Ай бұрын
Дайте угадаю: через логорифмы?
@recepgurkanhosman155
3 ай бұрын
Cevap 1 oluyor 2 üzeri 5 x in üzeri 32 den x le 2uzeri 5 yer değiştirme yaparak üste 5 üzeri x kalır oda x sıfır dan 2 ye eşitlenir.
@aneedfortheory
2 ай бұрын
If you need to resort to manipulating in the way that you did, I think switching to logarithms is far easier. You simply have to find a multiple of 32 that includes as a factor a log to the base of 2 that generates itself....namely 256, which is 32 times log to the base 2 of, you guessed it, 256. If the kids are in the Olympiad selection process, that kind of arithmetic via logs is child's play to them.
@mohamedmortady6325
Күн бұрын
Ln both sides bro
@Alex_the_engineer737
3 ай бұрын
Если расписать левую и правую часть как функции, то за счёт чётности, функция f(x)=X^32 будет пересекать функцию g(x)=2^x в двух точках: одно решение потеряно. P. S. ради интереса забил в Desmosе эти 2 функции и абсциссы их пересечений равны 1.022 и -0.979. Вот так вот интересно.
@K.Klogic
3 ай бұрын
Good work
@ЛарисаРашевская-э3щ
3 ай бұрын
Думаю, что не ординаты, а абсциссы, но их три, еще 256
@Alex_the_engineer737
3 ай бұрын
@@ЛарисаРашевская-э3щ Спасибо, исправил
@Swamisonic18
3 ай бұрын
@@Alex_the_engineer737 Yes same bro, but i can't find x= 256 in desmos plotting, why so? It shows only 2 intersections😢😢
@Alex_the_engineer737
3 ай бұрын
@@Swamisonic18 Most likely, this is due to the fact that the polynomial of the nth degree has at most n roots. In our case, this is a polynomial of the 32nd degree on the right side, which essentially limits the number of roots of this equation. That is, in this equation it has already been proved that there are at least 3 real roots, and all the others are complex. (Unless we find other real roots)
@KipIngram
11 күн бұрын
2^x = x^32 ln(2^x) = ln(x^32) x*ln(2) = 32*ln(x) x = (32/ln(2))*ln(x) x = e^((ln(2)/32)*x) A couple of iterations of the last one there yields x = 1.02239294025, which appears to be correct. Begin with x = 33/32, which is an easy to derive approximation (substitute x = 1+y and make the obvious approximations).
@K.Klogic
10 күн бұрын
👍
@jamesmarshall7756
4 ай бұрын
The difference between \(2^{1.0224}\) and \((1.0224)^{32}\) is approximately \(-0.00044\). This small discrepancy indicates that \(1.0224\) is a very close approximation to the solution of the equation \(2^x = x^{32}\). ChatGPT
@K.Klogic
4 ай бұрын
Thank you for your comment ❤️
@malinauagar4344
2 ай бұрын
This type of problem is still big problem fot gpt but it can solve it in the end, wiil wait fifth gen.
@Durga.Devi123
2 ай бұрын
Sir if there is any G chat available? Through gmail so can discuss further regarding to topic
@ahmadsyafrawi3499
Ай бұрын
Ini bukan penyelesaian
@純蛋白質
3 ай бұрын
Easy Question , you did it to difficulty.
@DumAndSmart
3 ай бұрын
256,1.022,-0.979
@K.Klogic
3 ай бұрын
Thank you for your comment ❤️💖
@qwer-vg6wj
Ай бұрын
Việt Nam chúng tôi gọi là đoán mò ra ta có :D
@AlfredoMartinez-hm2tb
3 ай бұрын
Es una solución para estos exponentes con otros exponentes no funciona, no es un método solo es una solución, con logaritmos es más fácil resolver este tipo de ecuaciones.
@flickmew99
7 күн бұрын
Idk why I laughed so hard😂
@K.Klogic
7 күн бұрын
Thank u dear
@fani_uye
Ай бұрын
Why the number keep getting bigger? N why equation is getting more complicated?
@tolniks
Ай бұрын
Это не единственное решение. Есть ещё два
@159phongsakornkawhaolai4
Ай бұрын
X = 0 You can try😂
@tshepomalalane4140
23 күн бұрын
Beautiful 🫡
@FarazBeg
2 ай бұрын
I don't mind the method, but do mind the time it took
@tihanyilaci
Ай бұрын
Wow. So X^2=2^2 means x=2 is the only solution?
@vildanatesoglu76
Ай бұрын
Ln: helloo
@MrPsubbara
2 ай бұрын
This equation has infinite answers. That's only one of the answers or roots
@eduardodavidsantacruzmacias
2 ай бұрын
No sé vio como resolvió al final
@K.Klogic
2 ай бұрын
Watch again
@psw8989
2 ай бұрын
밑2인 로그를 써라
@Durga.Devi123
2 ай бұрын
Great video, Sir how can we communicate with you regarding to any misunderstanding sie
@K.Klogic
2 ай бұрын
How can I help you?
@muzz1290
2 ай бұрын
X=1. Prove me wrong
@a_worldly_man
2 ай бұрын
You are wrong 2^1=2 1^32=1
@vanezaperalta4463
11 күн бұрын
💝💖🧡💛💚💙❣❣
@K.Klogic
10 күн бұрын
Thank u for watching my videos
@anurupdas9941
2 ай бұрын
By taking log this will provide trancedental equations to be solved graphically
@K.Klogic
2 ай бұрын
Good
@emrepoyraz53
2 ай бұрын
Like 1,022393
@Novomokoroni
3 ай бұрын
Ахуеть, и как я должен был это придумать?
@НашалабайРаджик
3 ай бұрын
Повезло, что показатель степени справа не 1024 😂
@ozencgencmert
3 ай бұрын
I solved this question using logarithms in 1 minute.
@K.Klogic
3 ай бұрын
Good work dear❤️💖
@hectoraular6180
3 ай бұрын
En ese caso no era necesario decir? que X diferente de 0 y X > 0
@vadimgerasimenko4904
2 ай бұрын
так себе...
@b213videoz
4 ай бұрын
x = 256 I'm finally starting to solve problems like this 😊
@K.Klogic
4 ай бұрын
Good dear sir 💖💕
@theophilusprat2202
3 ай бұрын
Why won't u explain and jus solving randomly
@K.Klogic
3 ай бұрын
❤️
@richardrakamazi5754
3 ай бұрын
x^(1/x) is a monotone decreasing function if x>e, then the equation x^(1/x)=2^(1/32) has at most one real solution. x=256 works, so no other real soultion.
@daniel-mircea
Ай бұрын
not at all. there are other two real solutions: x=1.022 and x=-0.979
@richardrakamazi5754
Ай бұрын
@@daniel-mircea ,,if x>e no other real solution than x=256
@Unf477
3 ай бұрын
Много лишних шагов
@meser1
3 ай бұрын
It is like a endless math nightmare 😄 but thanks 👍
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