In this video, I showed how to interpret and solve a tetration equation correctly using basic algebra.
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@The_Digital_Arts_World7 ай бұрын
In all of the math courses I have taken through graduate school, I have never heard of tetration. This is absolutely amazing, the instructor is extremely powerful and exciting and yes, even at 71 years old … i learned something. I know I have used the Lambert W function before in math and engineering.
@triggergaming711511 ай бұрын
You are not just a teacher, you are my inspiration to learn something new. Thank for it❤
@aroushansenthilkumar11 ай бұрын
I have an A level mock tmr , this has genuinely helped me understand logs and exponentials better now thank you
@PrimeNewtons11 ай бұрын
Good luck
@dereklenzen23307 ай бұрын
I have a MS in mathematics, and I have actually never worked with the Lambert W function before. (Though I did use tetration once to rewrite a function raised to itself.) You have taught me something new! Thanks for a great video. Subscribing. 🙂
@sobad293911 ай бұрын
Never stop learning those who stop learning stop living, what great words with your ability to make math as simple as possible ♥
@LukieReal5 ай бұрын
i absolutely love how familiar yet abstract this problem feels. such a cool solution. thanks for sharing!
@RootlessNZ3 ай бұрын
Thank you for your instruction. I too have learned something new at 78 years of age. I have just come across tetration for the first time and I'm fascinated by how you manipulate the above equations so expertly. I'm hooked.
@Lordiustofu7 ай бұрын
as a 13 year old, this video gave me a piece of mind of how math is really like, it isnt just numbers with the four operations nor sq roots, but it leads me to tetration, a whole new idea of how math works
@manyifung54117 ай бұрын
I’m 13 years old too!if you’re interesting in maths,I suggest you to learn calculus it’s really fun!
@prateek1.97 ай бұрын
@@manyifung5411 bruh why you 13 yr olds are getting into this complicated math thing ?you have a beautiful life to enjoy . also , you have to learn calculus anyways after 3 or 4 year later. why not enjoy now
@Dojaesd5 ай бұрын
@@prateek1.9 some people enjoy math yk.
@JaseewaJasee2 ай бұрын
the depth and breadth of your knowledge is amazing!
@BetaLoversYT10 ай бұрын
I am studying Economics at university, and, although this is the first time I see a video of yours, I feel I am going to use this eventually. Thanks for uploading it!
@ms_ks48 күн бұрын
Ok the fact that this guy is so talented he's making me feel like I can understand whatever the hell he's writing blows my mind
@Xnes__111 ай бұрын
You are a great teacher! Thanks for information.
@sonicwaveinfinitymiddwelle85554 ай бұрын
For moment I thought the question was wrong due to 2 superexponents in row but luckily this video explains how to really solve tetrational problem. Something new learned today.
@christopherrascon63866 ай бұрын
This is mind-blowing!!! 🤯
@haroldlake10055 ай бұрын
I am 72 and I´ve never heard something like this, tetration was unknown for me. always we can learn something new, Thank you.
@rajibchaudhury79744 ай бұрын
You are the only one who think out of the box, Newtons. Superb Video, yet again!!😃
@ibrahimyazici56516 ай бұрын
We need more teachers like him. And he should be idolized by many
@Kobe24SherlockHolmesChaitanya9 ай бұрын
Other than your amazing way of teaching and your enthusiasm, one more thig i like is the hats
@ZN9_xe11 ай бұрын
Man, your explanation are amazing ❤
@MathLover134 ай бұрын
The more I watch your videos the more inspired I get to learn more and more keep up the good work❤❤
@sourishnanda18099 ай бұрын
Craziest person on earth Love you bro ❤ Solving maths to the next level
@enzoys9 ай бұрын
but where does this W function even come from??
@budderman3rd4 ай бұрын
It's the inverse function of xe^x. Mathematician found there is no way to get x from xe^x, so they figured out what the inverse function would be and how it worked and called it lambert w function or product log. It became a useful function for solving certain equations.
@parigupta8601110 ай бұрын
Your videos always trigger the mathematician in me ❤❤
@aryatripathi248611 ай бұрын
How am I, an average 16 year old suddenly finding maths so interesting and dwelling more on it??? Edit: Any INTPs?😀
@HomieSeal11 ай бұрын
Because math is great!
@Bruh-bk6yo11 ай бұрын
Here comes algebra...
@mrchewy67911 ай бұрын
Because most sciences are actually fun when you know what the hell is going on
@samthedjpro11 ай бұрын
Same but 15 year here
@aryatripathi248611 ай бұрын
@@samthedjpro cooll! we can b friends!
@psevdonim7534 ай бұрын
Чел лучший гетеросексуально логарифмирует! Пик и Эльмир гордятся тобой!
@LucSzI11 ай бұрын
These videos truly resparked my interest in mathematics, thank you
@markfekete50789 ай бұрын
You have all the passion of the world and I really respect that. thx for this equation solving. I'm not a big fan of math but your presentationvwas really great.
@gunssom00784 ай бұрын
I got to ²x = 2, but didn't know Lambert W Function and couldn't solve it. Will watch that Video. Thanks for teaching this in a Clear and Straightforward way
@onyx_enigma10 ай бұрын
i mean i knew how ²x had to be 2, but i got stuck after that so i continued the video great explanation 👍
@scarletevans447411 ай бұрын
I tried to solve it in my head and ended up equating tetration with exponentiation, getting log(3) instead of log(2)... then, I immediately remembered what you said about our brains, at the beginning of the video! 🤣
@heco.10 ай бұрын
i solved it in my head too. took me like a minute since i am not really used to tetrations.
@williamkeitaro89104 ай бұрын
finally a teacher that doesn't unnecessarily overcomplicate things with the "a+b a/b (ab)" thing
@ГригорийФилипп-п9у10 ай бұрын
Since 3^3=27, 3^^2 = 27 (^^ equals tetration), and we should find x that, been tetrated to 2, gives us a 2, so it is just x^x=2
@gilmartrevisan8 күн бұрын
Very Nice class, Professor Tks
@kripaasp19 күн бұрын
After watching I am 40 years old again felling interst in mathematics. Thanks
@VanshikaRathod-v5bАй бұрын
You sir is great 🎉🎉 best thanks to your teaching skills, whenever i saw your video my reaction like 😮, thanks sir keep it up if you not make video my reaction like 😢, sorrry ok bye😅, thansk for 10 million likes to this comment
@corbonmaths95972 ай бұрын
Thank you to teach us some technics with non trivial operations !
@davestillhere41694 ай бұрын
Lovely, really nice to watch.
@ExpungedFunkyFriday6 ай бұрын
Make a video about every kind of exponential and tetration equations please
@redroach40111 ай бұрын
Omg i just came from your other video about x to the super power 2 equals 16 and used the same method to solve this and it took less than a minute. Thank you soooo much for yraching me this cool trick
@Khaled_HR13_kardashev3 ай бұрын
What an amazing guy!
@abumarwan610 ай бұрын
I love explaining mathematics - thanks for your efforts
@goabaonesekalaba2830Ай бұрын
Wow ❤This is amazing. Take your flowers 💐 brother
@gilmartrevisan7 ай бұрын
Nice example, Professor. Tks
@Mech14110 ай бұрын
x is 1 because 3 raised tetrated by 2 is equal to 3 to the power of 3 which is 27 and 3 tetrated by 1 is 3 so x=1
@tjahyotamtomo7189Ай бұрын
The difference between the solutions you mentioned-\( X = \sqrt{3} \) (approximately 1.732) and \( X = 1.56 \)-suggests that something might have gone wrong in the logarithmic approach that resulted in the value \( X = 1.56 \). Let’s carefully revisit the logarithmic approach to understand where any discrepancy might have arisen. ### Re-examining the Logarithmic Approach The equation we are solving is: \[ 3^{X^2} = 27 \] 1. **Step 1: Take the natural logarithm of both sides:** \[ \ln(3^{X^2}) = \ln(27) \] Applying the logarithm power rule, \( \ln(a^b) = b \cdot \ln(a) \): \[ X^2 \cdot \ln(3) = \ln(27) \] 2. **Step 2: Express \( \ln(27) \) in terms of \( \ln(3) \):** Since \( 27 = 3^3 \), we can write: \[ \ln(27) = \ln(3^3) = 3 \cdot \ln(3) \] 3. **Step 3: Solve for \( X^2 \):** Substituting \( \ln(27) = 3 \cdot \ln(3) \) into the equation: \[ X^2 \cdot \ln(3) = 3 \cdot \ln(3) \] Dividing both sides by \( \ln(3) \) (which is a positive number): \[ X^2 = 3 \] 4. **Step 4: Solve for \( X \):** Taking the square root of both sides: \[ X = \sqrt{3} \approx 1.732 \] ### Addressing the \( X = 1.56 \) Result If you obtained \( X = 1.56 \), this might indicate: - **An approximation issue** during intermediate steps. - **A calculation mistake** in how the logarithms were applied. - **A different interpretation** of the equation, which led to a slightly altered result. ### Conclusion The correct solution using either the pattern recognition approach or the correct logarithmic method should yield \( X = \sqrt{3} \approx 1.732 \). This matches the expected result when solving \( 3^{X^2} = 27 \). If you consistently get \( X = 1.56 \) using the logarithmic approach, there may have been a mistake in one of the logarithmic steps. Double-check the logarithmic steps to ensure they correctly follow from the given equation.
@carlossantosalmeida63966 ай бұрын
YOU*RE A CRAZY TEACHER! CONGRATULATIONS!
@elishagunasekara403822 күн бұрын
That was a great lesson!👍
@aryaprasad99749 ай бұрын
I have a doubt.. how would u solve this: ²2²? Which would u solve first the exponent or tetration?
@PrimeNewtons9 ай бұрын
That's an interesting question.
@venkybabu814010 ай бұрын
Super power is somewhat like double integrals and triple etc. because a super power series can always be replaced by integrals. Base depends on grains.
@A.A.A5436 ай бұрын
Is this comes in college level maths? Although I know how to solve it but I haven't learnt this in my school.
@dannygolds10 ай бұрын
I'm studying in Russia and I think we have so little knowledges for W-function, or our lecturers just dont' wanna to learn to us with it, jush perfect solution we suggested, master!
@heco.10 ай бұрын
You're absolutely right! We are learning so many complex algebra equations but not the LambertW function. And because of that we can't solve stuff like x^x = 2. I am in my last year of high school but we don't have LambertW function in college. So, I learned it entirely from internet.
@AbouTaim-Lille11 ай бұрын
Can you give more detalis on the Lambert W function. If it is just another special function it is ok but we need Its , properties, its division and integral. And Its taylor series.
@PrimeNewtons11 ай бұрын
Working on it
@tyal-q9x4 күн бұрын
Just found this channel. Interesting
@ModelTypeZero5 ай бұрын
i figured it was the square root of 2 from the 'therefore' step, is this not correct? (1.41)
@pierrettebalazut94078 күн бұрын
J'ai "vaguement compris,", mais je ne comprends pas ce que représente W? Et phi
@フミズ4 ай бұрын
How can we solve if the tetration value is a fraction like ½2?
@PrimeNewtons4 ай бұрын
It must be a positive integer
@_Diana_S11 ай бұрын
Where, in what science field, do we use tetration? What natural phenomena can be mathematically described by it?
@Wolfy-pw2py10 ай бұрын
Mathematician obviously since they deal with all maths related and probably math that involves studying space since the universe is infinite and involve big numbers like from billion up to sextillion and more light years
@igravity29655 ай бұрын
How can we visualize 3 tetrated to the 1.56?
@sudiptoatutube11 ай бұрын
First Comment! You are a great teacher.
@vorpal12011 ай бұрын
This was great! Thanks for sharing some under taught maths. No one ever showed me this stuff. I'm just playing here but, now for the sarcasm: Never stop learning? Those who never stop learning, forget. Those who stop learning, remember. Meaning I got a finite amount of memory and the more I cram in my head nowadays I tend to lose something else. But if I hold on long enough to what I know. I will remember those memories, longer. I just forgot where I put my keys.... bummer.
@JCSol3 ай бұрын
This is amazing.
@crowreligion7 ай бұрын
What is 2 tetrated to 1/2? Can we have a logical answer to this?
@aminniku689810 ай бұрын
Thank you, from Iran 🤗
@ryanchicago602811 ай бұрын
Looks like Lambert even got to spend time with Euler. Pretty interesting! They knew about non-Euclidean geometry.
@goabaonesekalaba2830Ай бұрын
I didn’t know this channel!
@TheMathManProfundities7 ай бұрын
A word of caution here, you explained the original left hand side as being ²(3↑↑x) when in fact it is 3↑↑(²x). You demonstrated this correctly when you equated 3↑↑(²x) to 3↑↑(2) but your expansion was wrong.
@TheMathManProfundities7 ай бұрын
Typo: meant to say explanation not expansion
@DSN.00110 ай бұрын
How parenthesis work in tetration, from up to down or vice versa
@MOVIEPARADISE1211 ай бұрын
Pls explain about the pentation
@aryatripathi248611 ай бұрын
hahahha ur like mee
@אבאאבא-ע1מ9 ай бұрын
Superlog of both sides with base 3 could also eliminate the base 3 on both sides
@mrsadmangaming635011 ай бұрын
um bro what if the tetration is in the negetive so i mean that what if it was said that 3 raised to the super power -2 . how would u define it?
@freddier4711 ай бұрын
I remember reading somewhere that we haven’t defined tetration for non-natural numbers yet but I can’t remember where I read that so that could be a complete lie
@mrsadmangaming635011 ай бұрын
okh bro still helpful tho :)@@freddier47
@ryanman008311 ай бұрын
@@freddier47Real numbers are defined We can understand better with super Logarithm (inverse of Tetration) By definition sLog2 (2^^3) = 3 NOTE: "sLog" is a notation for super Logarithm. Like how Logarithm cancels the base leaving the exponent ex. Log2 (2^3) = 3 super Logarithm does the same with Tetration leaving the super power. We can use super Logarithm to solve non integer super powers since super Logarithm is repeated Logarithm by definition. Let's let sLog2 (16) = 3+x Where 0 ≤ x < 1 (represents a 0 or decimal) sLog2 (2^^3) = sLog2 (2^2^2) => Log2(2^2^2) = 2^2 => Log2(2^2) = 2 =>Log2(2) = 1 At this point we've taken three logs representing our integer part of the solution (given by the fact that the answer is equal to 1). We just take log again for the decimal x (the remainder of 2's that we need.) Log2 (1) = 0 Thus sLog2 (16) = 3+0 = 3 Well let's look at what happens when we go backwards through the same process to see what happens to the remainder. Log2 (Log2 (Log2 (Log2 (16)))) = 0 Log2 (Log2 (Log2 (16))) = 2^0 Log2 (Log2 (16)) = 2^2^0 Log2 (16) = 2^2^2^0 16 = 2^2^2^2^0 = 2^2^2 = 2^^(3+0) The remainder adds an extra '2' to the top of the power tower and the additional 2 is raised to the power of the remainder For 0 ≤ x ≤ 1 By definition sLog a(a^^3+x) => a^a^a^a^x By definition of Tetration a^^3+x = a^a^^2+x = a^a^a^^1+x = a^a^a^a^^x a^a^a^a^^x = a^a^a^a^x a^a^a^^x = a^a^a^x a^a^^x = a^a^x a^^x = a^x by definition for 0 ≤ x ≤ 1 We can take for example 3^^e ≈ 3^3^3^(e-2) ≈ 227,914.4 It's complex numbers (i.e. 2^^i) that it's not defined
@ryanman008311 ай бұрын
For real numbers a^^x = a^x for 0 ≤ x ≤ 1 for negative super powers we use the above definition to extend to negatives -1 ≤ x ≤ 0 a^^x = Log a (a^^x+1) NOTE: because -1 ≤ x ≤ 0 then 0 ≤ (x+1) ≤ 1 thus the above rule applies a^^x = Log a (a^^x+1) = Log a (a^x+1) = (x+1)*Log a(a) = x+1: For -1 ≤ x ≤ 0 a^^-2 is undefined because a^^-2 = Log a(a^^-1) and a^^-1 = 0 by definition so a^^-2 = Log a(0) and you can't have 0 in the Log
@nzqarc10 ай бұрын
@@ryanman0083 actually, complex numbers have been defined too.
@samthedjpro11 ай бұрын
How we can build exponents with decimal numbers , like x superpower 3 is ((x power x) power x) but what would be x superpower 1.56 ?
@nzqarc10 ай бұрын
i think that has yet to be defined
@samthedjpro10 ай бұрын
@@nzqarc I thought so, asked my professor he said you don't need to know this 😑
@kimutaiboit851610 ай бұрын
I imagined such a problem. To keep it simple let's start with ½^X That will be 1/(²X) Now for 1.5^X it will be ³X/²X. Just my thoughts.
@samthedjpro10 ай бұрын
@@kimutaiboit8516 I also thought that but I was wrong as x time x is x² or x^2/1 and x^1/2 will be opposite which is how many times it should be multiple so it makes x which is √x but when we talk superpowers (supeman 😂) ²x will means x power x but x superpower 0.5 must means how many times x should be exponentiate to make x which neither logs or any function can define, if you have any answer please comment 👍
@kimutaiboit851610 ай бұрын
@samthedjpro let's say x=3 ²3 is 3³ ¹3 is 3 My claim was ½3 is 1/3³ But now that you mention it, I think I have to relook it. The expression I made is for -²3 I think ½3 is undefined as you said. 🤔 PS: What could ⁰3 be? I guess undefined too.
@kumar103611 ай бұрын
Great explanation
@helixfire11987 ай бұрын
I never learned lambert functions. is that calculus ? Also i barely remember log functions on my texas instrumemts calculator. Im going to watch videos on this. I wish this youtube channel was around years ago when i was in school.
@urs23573 ай бұрын
Super..
@bigobibishop11 ай бұрын
Great video
@stevenHUH10 ай бұрын
Well explained sir!
@Mehrdad_Basiry-fj4rl10 ай бұрын
Amazing...❤❤❤.
@elasmarsaadallah61268 ай бұрын
Bro !! I can't accept this solution until you define what is ˣa where x ∉ ℕ , please explain
@PrimeNewtons8 ай бұрын
x must be an integer
@infraredaustrian67147 ай бұрын
You... next level!
@jonathanmulenda86683 ай бұрын
I did it mental math without the Lambert fnctn: sqroot of 27=5.1962 , because 27 is what we get after the last super power then remained with 3^x=5.1962...x=logbase3(5.1962) and x=1.5 sorry I used a lot of space..... You're doing great cudos!!
@arminklar361310 ай бұрын
Wow good Präsentation
@Necrozene5 ай бұрын
Great stuff man!
@mrblakeboy142010 ай бұрын
you can easily see that you have to solve it as 3^^(x^x)=27 , which means you have to solve it as x^x=2. i don’t have enough math experience to solve it from there, probably something with e^ln(x^x)
@dilshad0038 ай бұрын
Beautiful !
@CC--qn4gf2 ай бұрын
We need more tetration problems
@QuantumCAT05 ай бұрын
I i had a tutor like you in school then was to be excellent in mathy
@210652211 ай бұрын
It was super! 😮 Thank you! 👍
@Hanible9 ай бұрын
I did it with mental math, x^x = 2 , because 3^3 = 27 => x = e^(W(ln(2)))
@PrimeNewtons9 ай бұрын
You are already a pro
@Hanible9 ай бұрын
@@PrimeNewtons I'm an engineer so yeah in a way I'm pro lmao nice videos you're a great teacher!
@Stn_47 ай бұрын
I wish if I had got one like you since I was in lower schooling system .. Ah !!!!!
@kimutaiboit851610 ай бұрын
Someome asked about 1.5^X I imagined such a problem. To keep it simple let's start with ½^X That will be 1/(²X) Now for 1.5^X it will be ³X/²X. Just my thoughts.
@sportsloverbaseball9 ай бұрын
I might be misunderstanding, but 1.5^x≠x tetrated to 1.5. It would be 1.5 to the power of x. For tetration, use ^^. For example, the equation is 3^^x^^2=27
@kimutaiboit85169 ай бұрын
@@sportsloverbaseball I see my error. Thanks.
@sportsloverbaseball9 ай бұрын
@@kimutaiboit8516 np :)
@PlatonAltei9 ай бұрын
So interesting
@nikkirolle70327 ай бұрын
Things I love!!!
@neevee_gd11 ай бұрын
the answer is 2? (first question)
@michaelbaum679611 ай бұрын
Great👍
@NameUV310 ай бұрын
1.5?
@y_us_1211 ай бұрын
Interesting what is super power of 1.5. Is it a power tower of height 1 and half 😮
@cosmicgarou9911 ай бұрын
This is heaven for me 👍, for the love of mathematics
@jbot81085 ай бұрын
nice video
@emmanuelpaygar373611 ай бұрын
Hi how can I go about to solve ˣ2=²ˣ7
@GodGapple6 күн бұрын
Never stop learning, because if you stop learning, you stop living