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
Пікірлер: 388
@gamertz5052 ай бұрын
Beside the math did anyone try to remove hair from screen like me in beginning?😂😂🤣
@RadicalCaveman2 ай бұрын
It's not a hair. It's a plutonium shaving.
@gamertz5052 ай бұрын
@@RadicalCaveman 😂🤣😂🤣😂🤣🤣
@justliberty4072Ай бұрын
I'm 63. I have a PhD in engineering. I've never heard of Lambert's W function.
@assiya3023Ай бұрын
العلوم في تقدم مستمر ، يجب علينا أن تحيين معلوماتنا دائما، ملحوظة أنا أيضا أبلغ من العمر 58 سنة ولدي دكتوراه في الهندسة الكهربائية . ولازلت أتعلم
@USCsteveOАй бұрын
@@assiya3023عمري 40 عامًا تقريبًا وأنا⚡ مهندس برمجيات. التعلم هو الطريق.
@donmoore7785Ай бұрын
I hadn't either, BS in engineering in '83.
@SebastianMedinaАй бұрын
Me too. Electronic Engineer '07
@AfricaWorldTV411Ай бұрын
Same here 42 years old,but it's always good to learn
@Akenfelds12 ай бұрын
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.
@donmoore7785Ай бұрын
Not only that, but how one finds complex solutions involving the Lambert W function. He pulled that from somewhere.
@svenbalzer6763Ай бұрын
Hello, It’s Only forn Part Highierer Like int Realschoolniveau Perhaps. Formytaste Is This Not Highschool or Studyniveau. Lg Sven BALZER
@ChrisBoshuizenАй бұрын
I came to say the same thing. But I'd say it's more like mindlessly rearranging the table place setting, and then pulling a fully made ham sandwich from the fridge. Very disappointing video.
@yama848317 күн бұрын
There is not really a lot to explain about the Lambert W function that is actually useful for the purposes of the video. It is simply a function that, for any x that can be described as x= a*(e^a), W(x)=a. It is actually a multivalued function, due to the nature of complex logarithm, but most of the time people focus on the principal branch, and with the exception of one, all other branches only produce complex results. It is also sometimes called the product logarithm. It has applications in higher levels of physics, mathematics and statistics, but it is not really ever taught outside of university, and even then only in the fields that actually use it. Nobody calculates W(x) by hand; it cant be articulated using elementary functions and can only really be explained as the converse relation of f(x)=xe^x; and is almost always kept in notation in Mathematics. The only other thing that would actually be useful to elaborate is that it is, for the principal branch, only defined for x ≥ -1/e in the real numbers, if you go below that value the results are complex numbers, which does happen in the video.
@StatisticalLearner2 ай бұрын
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.
@javgrzgАй бұрын
You nailed it mate
@shashwatraj2381Ай бұрын
Tldr?
@billwindsor4224Ай бұрын
@StatisticalLearner I agree with @javgrzg, excellent elaboration on the Lambert W function and Euler’s and Dirac’s work, thank you.
@billwindsor4224Ай бұрын
@@shashwatraj2381 As you progress in math, you will find it necessary to read and compute complex material. Check out the works of Srinivasan Ramanujan.
@rorydaulton68583 ай бұрын
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.
@onradioactivewaves3 ай бұрын
...and so 4ᵗʰ.
@papkenhartunian1862 ай бұрын
How do you find complex roots?
@rorydaulton68582 ай бұрын
@@papkenhartunian186 (My previous reply seems to have disappeared.) I used the SciPy package with the Python programming language. Search for Scipy and Python for details. I do not seem to be able to paste the relevant URL here. The WolframAlpha web site can also calculate values of the Lambert W function: just use the name "productlog" for the function. I have not yet figured out how to get WolframAlpha to choose a branch of that function other than the main branch.
@BSnicksАй бұрын
Take it easy on him. I don't think he understands what the Omega function is yet.
@onradioactivewavesАй бұрын
@@papkenhartunian186 research the Lambert W function, that is the solution.
@PNLMathsАй бұрын
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.
@Russ--R19 күн бұрын
I'd stick the two functions in Excel and have a look at where, if at all, they cross.
@VengerVideoGamer18 күн бұрын
Exactly. I did my maths degree 30 years ago and never once came across the Lambert W function as it seems that it's not widely taught. Indeed, this is what Wikipedia has to say about its usage : In 1993, it was reported that the Lambert W function provides an exact solution to the quantum-mechanical double-well Dirac delta function model for equal charges-a fundamental problem in physics. Prompted by this, Rob Corless and developers of the Maple computer algebra system realized that "the Lambert W function has been widely used in many fields, but because of differing notation and the absence of a standard name, awareness of the function was not as high as it should have been."
@olmynuwen3 ай бұрын
Somehow I do not feel enlightened
@PavelKucera-bd9dd2 ай бұрын
Sorry, but 4^(-0.0887+1.512i)=-0.4434+0.765i. 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 4^(1.248-5.505i)=1.248-5.505i.
You have explained an answer that does not exist. You have not explained how you found the complex solution.
@KLONDYKE11112 ай бұрын
You speak too fast!
@BSnicksАй бұрын
LOL
@zdrastvutye2 ай бұрын
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 c=acs(csc):snc=sqr(1-csc^2):dg=c/snc/a^b:dg=dg-1:return 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 "exp(";b*ln(a);"+";ln(a)*c;"*i)=";b;"+";c;"*i or" 120 print a;"^(";b;"+";c;"*i)=";b;"+";c;"*i" higher mathematics-a beautiful math question 0.250501609 1.39285046 exp(0.347268968+1.93090073*i)=0.250501609+1.39285046*i or 4^(0.250501609+1.39285046*i)=0.250501609+1.39285046*i > 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
@winstongludovatz1112 ай бұрын
This is painful, the most trivial inequalities will show that there is no real solution. Higher mathematics?
@adrianlautenschlaeger85782 ай бұрын
I think it's not painful because of missing real solutions. The most equations/functions are really hard or impossible to invert. Popular example ist LambertW, the inverse funktion of xe^x Or try to invert a quintic function ;-)
@paulo332 ай бұрын
this is not higher mat .
@mathematicsquiz2 ай бұрын
kzbin.info/www/bejne/mHmuk5udd6Z1jtk
@LelekKozodoj69Ай бұрын
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).
@papkenhartunian1862 ай бұрын
Could you explain how you found the complex root?
@urban_sculptorАй бұрын
G**gle Scipy lambert. There's a good explanation and example how to find complex roots
@ajitandyokothakur71912 ай бұрын
You keep repeating "Natural log Natural log..."). It is probably your verbose but some might find it confusing. Dr. Ajit Thakur (USA).
@Anti-You2 ай бұрын
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.
@luckyluk4Ай бұрын
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 .
@mdrokebtamim648Ай бұрын
This question itself wrong. How it is possible to X is more bigger than X 😂😂😂. X=4^x impossible.
@antennaistАй бұрын
Exactly.
@shipsahoy1793Ай бұрын
when mathematics becomes impractical, it essentially becomes a useless waste of time .
@peterreali3950Ай бұрын
@@shipsahoy1793 x = -1/2 is the simple solution -1/2 = 4^-1/2 = = or - 1/sqrt(4) = + or - 1/2 choose negative root so x = -1/2
@student6140Ай бұрын
Not if x is 0
@shipsahoy1793Ай бұрын
@@student6140 if zero is the only solution, then what's the point of the equation, other than noting a specific math property ? ..Mathematics consists of properties, identities, rules, and procedures, etc. but exists for the purpose of actually quantifying real world phenomenon, or solving math equations that get you there. There really is no point to an equation like the one written here, other than to say any integer to the power of zero equals zero.
@nooruddinbaqual78692 ай бұрын
Lambert W function is confusing Is it of any practical use or serves as brain teaser only?
@bookashkinАй бұрын
W is defined as a compositional inverse to a more familiar function. Shorthand (so yes, practical). For example sqrt(x) is shorthand for a number a such that a^2=x. Arctan(x) is shorthand for a number a such that tan(a)=x. Ln(x) is shorthand for a number a such that exp(a)=x. W(x) is shorthand for a number a such that a*exp(a)=x.
@xypherdrakeinsignia21Ай бұрын
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
@achomik1999Ай бұрын
so u input x=1/2 and output x=2? lol this isn't c++
@skateordiee2 ай бұрын
Wait, I think I figured it out… X = X lmao 😂
@vreveyvin-uw8umАй бұрын
error : can't solve
@franzxavereiholzer84992 ай бұрын
The numeric solution he gives is wrong
@GuoweiMa-k9t25 күн бұрын
Every time i can't get into sleep then i choose ur video😮
@tuho2977Ай бұрын
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.
@CLOVERYAU14 күн бұрын
No real solution but it has complex solution as explained in the video.
@zunden2Ай бұрын
Pertanyaan ini tidak ada hasil jawaban, meskipun x sebelah kiri bernilai 0, x di sebelah kanan bernilai 1, tapi bila x sebelah kiri bernilai -1/2 maka x sebelah kanan bernilai 1/2.
@padraiggluck29803 ай бұрын
The graphs of the functions y=x and y=4^x do not intersect.
@jstarks1232 ай бұрын
Which is why the solutions are complex.
@padraiggluck29802 ай бұрын
@@jstarks123 R2 is isomorphic to the complex plane ergo the graphs do not intersect there either. The only ‘solution’ is bogus.
@spacelem2 ай бұрын
@@padraiggluck2980y=x²+1 and y=0 do not intersect in R² either, and yet we know that intersects at the points (±i,0).
@padraiggluck29802 ай бұрын
@@spacelem x^2+1 has nothing to do with the given problem.
@spacelem2 ай бұрын
@@padraiggluck2980 except that it fits the same properties you gave for saying "the only 'solution' is bogus".
@question1answer1Q1A1Ай бұрын
2^x = x , if we put x = 0 + 1i then 0 + 1i ≈ 1 ,
@jordansmirnov72912 ай бұрын
What a boring explanation....
@oromath2 ай бұрын
Needing only one line !!!!
@KhinMaungSan-qc9uvАй бұрын
a^2--b^2=(a+b)(a--b) type must be used.
@yogesh1930012 ай бұрын
I feel Lambert W is just a cheat😂😂
@bookashkinАй бұрын
Sure, but so is the square root function :)
@packerfan201023 күн бұрын
so are the complex numbers lol. They were literally invented to solve the equation x^2 = -1
@AjitKumar-zs3hqКүн бұрын
Bro just draw a graph 📉 and you will get that both of the equation would never meet each other
@spacelem2 ай бұрын
"natural log natural log 4" is ln(ln(4)). This would be very difficult to follow along with just the audio. Just say "log 4", we know it's base e.
@RexxSchneider2 ай бұрын
The part which was missing was any proof of the assertion (around <a href="#" class="seekto" data-time="454">7:34</a>) that the graphs of y=4^x and y=x have no intersection. It turns out that y=a^x and y=x have no intersection when a is larger than about 1.44, but there is an intersection for smaller values of a. If you've spent time looking at these sort of problems, you would know that y=4^x and y=x have no intersection, but to baldly assert it is a flaw in the presentation.
@Mauro001-k2fАй бұрын
There is an error. W(-ln(4))= - 0.0881 + 1.5122i and x = 0.06396 - 1.09084i
@春-i4z29 күн бұрын
You are right. I'll show other solutions as well. Due to space constraints, I'll only list 10 of each. There are an infinite number of solutions. Since e^(θ) is a periodic function, so there are essentially an infinite number of solutions to this form of the equation. . W(-In(4))(1):-0.0886671243590498+ 1.51223002176232i and x(1):0.0639598103013431 -1.09084337653996i W(-In(4))(2):-1.73065765066981+ 7.63096008347849i and x(2):1.24840560504894 -5.50457413482802i W(-In(4))(3):-2.32409123809111+ 13.9723408498764i and x(3):1.67647745188376 -10.0789134268635i W(-In(4))(4):-2.69214366225873+ 20.2884293794372i and x(4):1.94197115545065 -14.63500822657i W(-In(4))(5):-2.9601591207798+ 26.592679120478i and x(5):2.13530344189561 -19.1825631455326i W(-In(4))(6):-3.17117931244319+ 32.8906040048285i and x(6):2.28752233391577 -23.7255556448044i W(-In(4))(7):-3.34528417340961+ 39.1847425656504i and x(7):2.41311244367119 -28.2658168889873i W(-In(4))(8):-3.49350176647778+ 45.476423994324i and x(8):2.52002883691722 -32.8043056869876i W(-In(4))(9):-3.62254983713748+ 51.7664139117173i and x(9):2.61311734270573 -37.34157431752i W(-In(4))(10):-3.73682704372826+ 58.0551859548791i and x(10):2.69555092232333 -41.8779644374954i . That's all. Thank you.
@春-i4z29 күн бұрын
A little more information: . In 4^(a+bi)=4^(a)*4^(bi), the period of 4^(bi) is 2π/(ln(4)). Here, 2π/(ln(4))=4.532 Calculating the difference from the solution for x shown earlier, x(9)-x(8)=0.093+4.537i x(10)-x(9)=0.082+4.536i Each difference in the imaginary part of the solution is almost equal to the theoretical period (2π/(ln(4))=4.532). . In other words, there are an infinite number of solutions for this period. . That's all. Thank you.
@marcusray1638Ай бұрын
4 = x/logx ,the standard decreasing function for all x greater zero. by graph or try and error. it is easy to get the answer easily 😂!
@OkulMuduruZeytindal2 ай бұрын
كيف يتم حساب. ( ) W رد ❤
@tungyeeso36372 ай бұрын
As usual, I would prefer using the graph approach. Since the answers are approximates, a graph works a lot simpler. 😊
@YassJ-jd5szАй бұрын
No ones knows about this W function. I think it would have more interesting to ask to prove that there is a unique solution instead.
@eovoosАй бұрын
Why isn't there a simpler way to solve it using simple algebraic formulas?
@ffggddss2 ай бұрын
Even by just imagining the graphs of y = 4ˣ and y = x, you should be able to see that they don't intersect, and therefore, there can be no real solutions to 4ˣ = x Any solutions must be complex, non-real. I suppose you could let x = re^(iθ) = r cosθ + ir sinθ or just x = u + iv, and take it from there. Looks like this is heading into Lambert-W function territory, which in complex space can get complicated. Let's see what the video does with it . . . Fred
@undecidable2 ай бұрын
You take time to explain the most rudimentary algebraic steps, but fly over the use of W. Come on...
@donmoore7785Ай бұрын
Yes he explained middle school math steps but brushed over Lambert W and in particular finding a complex solution.
@verdergreen32Ай бұрын
Such a task will never appear in reality and such an answer is of no use to anyone, because what to do with it?
@ghostsofbeauty.93462 ай бұрын
of two poss. answers i find here. 1 is. 4x. 2 is. 4x =x x= ?..
@Kanal2633 ай бұрын
Es gibt keine reelle Lösung. Das wird durch eine Kurvendiskussion von f(x) = 4^x - x deutlich.
@noname-ed2un2 ай бұрын
Can you please explain this statement. I don't understand
@noomensaidani131Ай бұрын
Parachuted responses. What is w fonction, in which field you've applied ln on x...... Etc
@FocusLRHAPАй бұрын
What about x^x = x? Only 1 as an answer? Only real one?
@春-i4zАй бұрын
x=1, or x=-1, and real solution only
@giovanniviglietta7312 ай бұрын
This is NOT a math olympiad question. This is the opposite of a math olympiad question.
@leolacic94422 ай бұрын
ha ha ha ha ha ha
@giovanniviglietta7312 ай бұрын
@@leolacic9442 What's funny?
@محمدالزريقات-ز1هАй бұрын
Can't we suppose that x is infinity?
@kopi3142 ай бұрын
Why ln and not log2 or log4 is used.
@dr.rolandzagler883117 күн бұрын
Hello, this is a nice equation with a expectable complex solution. I enjoy it. Nevertheless plz can you proof your complex value: Wolfram Alpha gives 0.06346 - 1.09084 i. The same value I obtain by calculating x = -W(-ln4)/(ln4) in solving your eq. with a second method (Initial deviding the eq. by 4^x.) Many greetings - Roland
@svenbalzer6763Ай бұрын
Hello, Why Sightsout all Questions like int Mainschoolniveau Perhaps, int Realschool ist Mathsquestion Ten Times Longer Perhaps. Myselfs didn’t Understand Why ITS‘S. Lg Sven BALZER
@SekiroEnjoyer123Ай бұрын
Another stupid question from this channel with the stupid Lambert's W function. Just change your channel name to "Lambert's W function".
@sergeisychev68242 ай бұрын
Let’s calculate and verify if 𝑥 = - 0.0887 + 1.512 𝑖 is indeed a solution to 4^x=x -- The evaluation of the equation 4^x=x with x= - 0.0887 + 1.512 𝑖 yields: Left side (4^x): - 0.4434+0.7651 𝑖 Right side (x): - 0.0887 + 1.512 𝑖 Indeed, it’s not a solution. This verification suggests that the complex value proposed does not satisfy the equation under standard complex arithmetic. -- Moreover, I can give an analytical proof that this equation has no solutions: separately for the entire set of real numbers and separately for complex ones.
@makehimobsessedwithyou64122 ай бұрын
Why not using log
@noname-ed2un2 ай бұрын
I thought about that at first. But after trying to solve it I couldn't find an answer
@stancatalina81632 ай бұрын
Autocomplete my search, in your way, 4 times
@einsteinalbert3099Ай бұрын
😂😂😂😂 will solving this maths in school provide a mansion and wealth like Jeff bezos 😂😂. Waist of time and brain.. in my country Nigeria we are only intelligent in making Dollars and working harder.. mostly eastern parts of Nigeria 😅
@weimenli7342Ай бұрын
We were promised a beautiful equation. What we got was a monstrosity with no apparent analytical solution, instead requiring some obscure function to be defined. Are math Olympiad people supposed to have written the Lambert W function in their solution? Or somehow calculate the approximate solution with numerical methods? Venting after spending 4 hours on this and finding there was no solution that could be done by hand after all 🤡
@bigscrounger3 ай бұрын
Is there a reason why you keep saying 'natural log natural log 4'. It's just supposed to be said once, unless you're applying the function twice...
@JTBettencourt2 ай бұрын
Yeah. That was weird.
@spacelem2 ай бұрын
I kept hearing that too, came to the comments to mention it. Personally I'd just skip the "natural" part after the first time and just say "log x", unless we change base.
@DarVV2 ай бұрын
Some tree logs laying in a park or forest are an example of the nature 😊 All of you have right about it. We should simplify our speech. Math itself can be complicated on academic level. Sometimes some blind people can hear this video too.
@jakemccoy2 ай бұрын
@@spacelemMost students learn that “log x” is assumed to have base 10. It would not make sense to clear up the language only to cause potential confusion elsewhere.
@spacelem2 ай бұрын
@@jakemccoy do they? I have a maths degree and I don't remember at any point log being assumed to be base 10. Even at school.
@mariem660528 күн бұрын
Isn't it easier to draw graphs
@user-mchlnwekrrrwq2 ай бұрын
mathematics: no room for error higher mathematics: *excist*
@jeannieheard1465Ай бұрын
Was there ever a mathematician with a sense of humor? OK, Einstein.
@rafadamian93992 ай бұрын
crap,the curve y = 4 exp. x has no point in common with the line y = x therefore the task is unsolvable.Never don't solve tasks that are unsolved /becauce you want to be clever/.the end
@JUSTREGULARSCREAMINGAAHH12 күн бұрын
This guy is an absolute fraud. He overcomplicates things to look smart, not realising he's a teacher
@cristianrolon7543Ай бұрын
Una reverenda estupidez esa "ecuación " no tiene solucion y esto se puede demostras de manera simple .. solo hay dos posibles exponentes que puedan satisfacer esa ecuacion y es 1 y 0 .. 4^1= 4 Y 4^ 0 =1 ESTO LO PUEDE VERIFICAR O RESOLVER UN ESTUDIANTE DE PRIMARIA ...
@sekjenbatuАй бұрын
No solution for real number.
@ptrblz2 ай бұрын
Nice, now if you rotate the linear function a bit you might get one or two real results, I was interested whether I can find the tangetial one and it seems I did for equation 4^x=e*ln(4)*x there shouod be just one real solution
@jim23762 ай бұрын
Mr. Lambert enters the room.
@QuojoK3 ай бұрын
Stop the over explanation. This should not take 10 mins
@notnow73022 ай бұрын
Bro why the hate? Its better to give more explanation than not giving any at all
@taoufiqhdach19052 ай бұрын
More explanation = More money 🤑
@progr61712 ай бұрын
Наши русские хитрозадые математики уложились бы в минуту)
@winailerdkasamsont27682 ай бұрын
I love this explanation at all .Don't judge wasting descriptions your time because you've already known .
@sugirib.a73022 ай бұрын
..searching money conten.....
@simokhaoua9496Ай бұрын
x=-0.0887+1.512i is not a solution 4^-0.0887+1.512i = −0.4741+0.7472i Clearly, 4^x ≠ x since the values do not match. The values differ considerably in both real and imaginary parts.
@春-i4zАй бұрын
This is a solution for W(-ln(4)), but not for x. The value we are looking for is X = 1/e^(W(-ln(4))). W(-ln(4))=-0.0887+1.512i Therefore, X = 1/e^(W(-ln(4))) =1/e^(0.0887+1.512i)=0.06396 -1.0908i This value is one of the solutions the author should be looking for. Therefore, the following relationship holds: 4^(0.06396 -1.0908i)=0.06396 -1.0908i. That's all. Thank you.
@truthseeker5971Ай бұрын
Why Einsten he persanaly admited that he wasnt good im math his first wife was she teached him to pass exams on university
@JacobWakem2 ай бұрын
You can also solve this using an infinitary expression and finding the fixed point.
@PeterPiedPiperАй бұрын
It is obvious that the left side is always greater than th right size. Please stop with these trivial questions!
@bgkim484318 күн бұрын
There's no point of intersection of two graphics Y=4^x , Y= x
@KeshavKashyap03Ай бұрын
Answer can be infinity value of x 😂
@musabsaleem361115 күн бұрын
Can you solve this equation: 9x square + 21x -8=0
@audreydaleski1067Ай бұрын
Interesting. Ln x =1
@fernandoangulo19602 ай бұрын
Hello, According to the fundamental theorem of algebra, a polynomial of the fourth degree must have four roots, including real and complex roots. Where are the other three roots?
@imperialblast2 ай бұрын
Theres no polynomial of degree 4 here (notice that it’s in the form a•b^x, whereas for polynomials all terms are in the form an•x^n)
@Shuparky6 күн бұрын
2x-3=5 X!=? Solve carefully 👀
@aliabbasmash786Ай бұрын
what is Einstein pic doing in thumbnails, he was a scientist not a mathematician.
@АртемХарченко-й3б2 ай бұрын
The solution can be easier determined by grafic
@lloydbotway5930Ай бұрын
Too much explanation of simple stuff. Not enough explanation of hard stuff.
@nayeemsschool1653Ай бұрын
haven't you studied Cambridge syllabus? simply use iteration method. its done
@stonecastle858Ай бұрын
Why do you keep saying natural log natural log four?
@zdrastvutye2 ай бұрын
i have changed that code a bit 10 a=4:print "higher mathematics-a beautiful math question" 90 c=acs(1/ln(a)): b=c/ln(a)/sin(c):print b,"%",c: 100 print "exp(";b*ln(a);"+";ln(a)*c;"*i)=";b;"+";c;"*i or" 110 print a;"^(";b;"+";c;"*i)=";b;"+";c;"*i" this question will become really difficult if a in line 10 is smaller than exp(1), so cos(e+f*i)=d (with d>1) cos(e)*cos(f*i)-sin(e)sin(f*i)=d and now there is a relationship between cos and hypcos as well as sin and hypsin via the imaginary number "i"!
@sam_sa4487Ай бұрын
I'M HERE TO TELL YOU THAT IN THE HISTORY OF MATHEMATICS THIS IS AN IMPOSSIBLE EQUATION
@ANIMEPLANET-t4n11 күн бұрын
ayo imo problems are infinitely more harder than this
@Santhoshkumar-ku1jgАй бұрын
why Einstein's picture neer this..was he a stupid 😮
@ioshift2 ай бұрын
The minimum value of lnx/x is 1/e
@hefazlalaАй бұрын
I have solved this one, sometime ago very easily. This does not belong to higher mathematics.
@SylvainKnowsITАй бұрын
Nice reminder. But could you point me to some material explaining the W function?
@LelekKozodoj69Ай бұрын
Wikipedia. Lambert W function.
@SylvainKnowsITАй бұрын
Thanks, @@LelekKozodoj69
@avinashm7423Ай бұрын
X=-0.5 seems to a solution to me. The square root of 4 can also be -2 also try once
@Andrew-II27 күн бұрын
I found a solution in parametric form: x = a + i * sqrt(4^(2*a) - a^2), where a is any real number. I did not use the Lambert-W function, only the Euler transformations, under the assumption that x is a complex number of the form a+i*b. It really works, I've checked numerically.
@tonimarie8951Ай бұрын
X=2 then? Thats what got without the messing..
@FiruzaSharabitdinova-ph6xv19 күн бұрын
Этого можно решать графический легко, и решение нет,зачем столько воды
@Gnowop3Ай бұрын
Why make it so complicated if it is required to be in the Real Domain. Just reason from the two curves of y=4^x and y=X and they dont intersect and hence no real soultion
@progr61712 ай бұрын
А не проще ли было графики построить?
@RoseRockefellerАй бұрын
I don't understand you talk too fast
@BSnicksАй бұрын
No, the guy doesn't even understand it himself, which is why he said a lot of rubbish. I tried to follow his calculations, but I was lost too. Even though I already knew about this product log function.
@AI_Look_Girl_2023Ай бұрын
The result I calculated using the AI program is: around X≈0.05
@lecombustor35712 ай бұрын
Why not solve for derivative of 4^x-x. Find zero value, so function minimum. Calc that value is positive. No real solutions. Forcing of lamber function in simple tasks is excessive.
@spacelem2 ай бұрын
It did say this is an Olympiad question. It's not meant to be trivial.
@n00bxl712 ай бұрын
The objective is not to find the minimum point
@mas-sk3pw2 ай бұрын
But don't you need to show that the zero value of the derivative occurs at a minimum and not a maximum of the function?
@n00bxl712 ай бұрын
@@mas-sk3pw Again, you're not looking for a stationary point at all. You're looking for the point it intersects zero, which it doesn't. Hence the use of the Lambert W function.
@mas-sk3pw2 ай бұрын
@@n00bxl71 But the idea of lecombustor's proof, as I understand it, is to show that 4^x = x has no real solution by showing that 4^x-x never goes down to zero, which in turn is to be proven by the fact that the value of y= 4^x-x is positive even at the lowest point on the curve, where dy/dx = 0. To my reasoning this requires showing that the curve y = 4^x-x does indeed have a MININUM (and not a maximum) value at the point where dy/dx = 0. As far as I know, this could be done by determining the direction of the concavity at that point using the second derivative of the function. Or am I missing something?
@Hellspawn100Ай бұрын
Never heard of the Lambert function as my peers. I'd probably go with a graphical method with the assumption that x € R. And if I go down that path this equation has no real solution.
@mahmudumurzaqov2487Ай бұрын
Не видели пациентов из психушку? 4^(-0.5i)=0.5i. не надо мучить голову.