@@timherrmann4168 did you already forget your first comment? I'll refresh your memory You wrote" what is 40^40" (Which is irrelevant when OP stated "you can solve this equation easily by just looking at the options-you wrote another problem without giving any options rendering your original comment redundant) I was offering you an opportunity to correct your initial mistake (or you're just aimlessly posting the equation because you don't know how to solve)
@@timherrmann4168 what specifically made you think "I didn't think for even a second before writing". I wrote so much because it seemed you forgot what was previously typed in the thread. Writing another equation with no context is hardly a viable way of proving a point. One cant easily deduce that in the context of OP's original comment you were implying "way too large to approximate in your head". With that being said my original comment of "what are the options" went over you're head so can I assume based off your reasoning you also don't think for a second before writing?
@@timherrmann4168 you are wrong. 40 is equal to 2×2×2×5. So that means if this answer is correct; then the right side of the equation also must have both 2 and 5 multipliers. But it doesn't have. So you can eliminate all options that has any other multiplier aside from 2. (Non-Prime numbers doesnt count)
@@timherrmann4168 lol OK champ whatever you say. "NEVER ARGUE WITH STUPID PEOPLE. THEY WILL DRAG YOU DOWN TO THEIR LEVEL AND BEAT YOU WITH EXPERIENCE.”
@@SiddharthRaiyani for algebra and below most likely anything harder than algebra and you better let me have my calculator but tbh the question is extremely easy
@@sattickchanda8245 Disagree, i had to take engineering calculus I, II, and III in college all without a calculator. I also wasn’t allowed to use it for Differential Equations. Thankfully I was permitted to use a calculator for Numerical Methods though.
As an engineer, I would have used method engineers know very well about, eliminate options, guess, and hope it is the right answer. So thank you for showing the process.
You don’t have to hope , just remove the Teo options with a 10 on it because s the number on the right does not have a 10 as a factor , 8 is too small done , zero calculations
That the number you know because you have been taught but a person who is doing it for first tim need to do this process and also it's a proof that 256 is tha answer
@@riksarkar4343 not really, with just guessing and logic its quite easy to get the answer. A and B is too small, C is not in the 2^x (like 2, 4, 8, 16, etc.) and E is just absurd
For me, seeing that 2048 is 2 to the 11th power and then seeing the relations between the number 256 and 2048 was enough to confidently say that D was the correct answer.
@@FullmoonFoxx I was talking about math skill and not government's policy making....poverty elimination doesn't depend on individual skill alone....whereas individual skill is personal....and it is precisely to escape poverty many students work extra hard to excel at math and science in India....and many have escaped poverty as a result.
This question isn't hard at all. It can't be 0 or 69420 obviously, so it must be 40 or 256, and considering 256 is a power of two, it's pretty clear what the answer is
you could also do this by deducing that 0^0 is 1, 8^8 would be way too small, 40^40 and 69420^69420 (69420 would be too large aswell) don't have anything to do with a power of 2 so the only thing left is 256^256
@@ThatisnotHair does it matter? it would be either 1 or 0 so either way the result would be too small. Since it's undefined it isn't the correct answer
Two of the answers involve a multiple of 10, which can only be created by multiplying 2 and 5. We are only ever multiplying by 2 on the right side (2^x = 2•2•2•...), precluding those two options. 2^n≠0, when n is an integer, leaving only 8 and 256. 8^8 = (2^3)^8 = 2^24 256 is the only remaining option.
yeah its pretty ez. the right hand side is a power of 2 which is the only prime here. so the left hand must be a power of 2 the only number here is 256
Such questions can be solved easily by logarithm It would be easier if an inequality was mentioned So we would just use Jensen inequality Piece of cake ques
@@epikherolol8189 I mean usually when I see x^x complicated equation my first initial thought was just put ln(x) in both sides and work my way to make it as x*e^x so I can put the Lambert W function
@@firehalf2935 its not about how teachers teach, its about if they even teach. At my school most of the teachers don't try at all and I have to rely on the internet and textbooks to teach me most of the material.
@@wavingbuddy3535 It is easy bruh. Just eliminate the options. There's no way it would be A,B or E, that leaves only C&D. 40 to the power anything will always have an unit digit with 0 but 2 to the power anything can never be zero. That just leaves option D and that is correct.
I knew it would be much faster simply plugging in all the answers until it was right, but I found it much more satisfying to generalize the solution mathematically rather than simply guess. I started with a system of equations: x^x=(2^a)^b where ab=2048 and 2^a=b The end solution here would of course be "b", and "a" is some unknown introduced with the intent to be solved out. Knowing 2048 is 2^11, putting "a" in an assumed form of 2^c you can work through it to form 2^(2^c+c)=2^11 which simplifies to 2^c+c=11, and you can easily see that c=3. Plugging all the way back up you get a=8 and b=2^a=2^8=256
I remember taking the SAT and not knowing any of the math. So I just reverse engineered the problems using the options given and figured out how to do it that way. Then, when I started classes, they put me right into algebra 2. But in reality, I needed to be in pre-algebra cuz I never learned it before. Still passed the class but I had to go to tutoring every day because I didn't know the basic shit.
Passed my highschool psychics and some chemistry, by using reversed calculation, but wasn't multiple choices, I used the notations and knowing the relations, I knew how to get the formulas to calculate the process and get the answers! I don't like to memorize every different formulas, only memorized the main formulas which can derive into others 🤧😆 and I was one of the few who passed the tests without retaking ( 7 people out of 26 students at that time if my memory isn't trolling me 🤷😂)
@@anthonyJones-ll4eiCouldn't agree more, I just felt like school is just draining my time instead of teaching me (ngl sometimes I don't even had enough time to study in the library)
for any x^x = z equation, x = e^W_k(log z) or equivalently x = e^W_k(ln |z| + i(θ + 2nπ), and for any x^x = 2^b equation, x = e^W_k(b/log 2) or equivalently x = e^W_k(b/(ln 2 + 2nπi)) where W_k is any branch of the Lambert W function/product log and n is any integer, and θ is the argument/angle of the possibly complex number z or b, this means there are not only infinite possible values due to infinitely many multiples of 2πi, but also due to the infinitely many branches of the product log, also it's pretty rare to find an equation of that type with an integer solution. Note that you have a real solution to the equation only for any b/log 2 greater than or equal to -1/e. the way you solved the equation though, that's not how you solve equations and if it were different by one unit the method wouldn't hold
It's nice cause it shows the way how you'd solve it, but in a test, you basically wouldn't get all that time, so you go by elimination game, where it will just take you a couple of seconds really. 0 and 69420 are out just by looking. 40 is also out as we are only dealing with 2's here. 8 is too small. So that leaves us with 256.
You can solve this question easily by jus looking at the options
@@timherrmann4168 what are the options?
@@timherrmann4168 did you already forget your first comment?
I'll refresh your memory
You wrote" what is 40^40"
(Which is irrelevant when OP stated "you can solve this equation easily by just looking at the options-you wrote another problem without giving any options rendering your original comment redundant) I was offering you an opportunity to correct your initial mistake (or you're just aimlessly posting the equation because you don't know how to solve)
@@timherrmann4168 what specifically made you think "I didn't think for even a second before writing". I wrote so much because it seemed you forgot what was previously typed in the thread. Writing another equation with no context is hardly a viable way of proving a point. One cant easily deduce that in the context of OP's original comment you were implying "way too large to approximate in your head". With that being said my original comment of "what are the options" went over you're head so can I assume based off your reasoning you also don't think for a second before writing?
@@timherrmann4168 you are wrong. 40 is equal to 2×2×2×5. So that means if this answer is correct; then the right side of the equation also must have both 2 and 5 multipliers. But it doesn't have.
So you can eliminate all options that has any other multiplier aside from 2. (Non-Prime numbers doesnt count)
@@timherrmann4168 lol OK champ whatever you say.
"NEVER ARGUE WITH STUPID PEOPLE. THEY WILL DRAG YOU DOWN TO THEIR LEVEL AND BEAT YOU WITH EXPERIENCE.”
Bro had to include that 69420 in there 💀
Blud really has some dirty thoughts there 💀
He did not even do that, wytb 💀
@@s1lkks look at the E) option of the question.
total Dr Evil move.
Yea just pls 😂
when the game 2048 from 2016 comes in clutch 😂
You guys don't know about powers of 2 used in binary in programming.
Thats where I learnt the sequence lol
When you see the ram and you know it's 256
Engineeeing students: “alright I have 4 options to plug into my scientific calculator”
😂😊
Calculator are generally banned in exam.
@@SiddharthRaiyani not for engineering students
@@SiddharthRaiyani for algebra and below most likely anything harder than algebra and you better let me have my calculator but tbh the question is extremely easy
@@sattickchanda8245 Disagree, i had to take engineering calculus I, II, and III in college all without a calculator. I also wasn’t allowed to use it for Differential Equations. Thankfully I was permitted to use a calculator for Numerical Methods though.
“I don’t believe you, it’s 69,420”
Its not, it nears infinity
@@Odinh funny thing about infinity. The tier-3 Illions (which are like 2 to the trillionth power). Are closer to 0 than they ever will be to infinity
@@Odinh nothing is jear infinity also the guy who wrote it was Joking
@@Odinh how tf can something near infinity
lol
only when you teach with joy ,it becomes true education and you sir have done that very well on point~
It's a form of rhythm with keys that unlock.
OMG. this is so helpful. I like this kind of shorts so much
Sneaky way to put that 69420 🤣
Of all the things that just happened, THAT is what you paid attention to?😆📸📸
He only learned math just to put 69420.
This. This is thecway
We all need something to help us concentrate 😂
I didn't saw that until you've mentioned it. lol
As an engineer, I would have used method engineers know very well about, eliminate options, guess, and hope it is the right answer. So thank you for showing the process.
As an engineer, I agree 😂
You don’t have to hope , just remove the Teo options with a 10 on it because s the number on the right does not have a 10 as a factor , 8 is too small done , zero calculations
"Write down your thought process and how you got your answer"
Hahaha
Guess i'm an engineer
Math can be magic.
이런거 보면 아이디어라는게 얼마나 중요한지, 그리고 지능과 직관이라는게 얼마나 연관되어 있는지, 그리고 훈련된 창의력이라는게 존재하는지 등등을 알 수 있음..
Logarithms were invented in 1614
People in 1613:
Where do you use logarithm here?
@@vertun14 idk, i ain't seen exponential equations yet
@@carlosmuniz7467 well why did you comment that when you do not even know how to use logarithm here?
@@vertun14 Take the log of both sides with base 2? At least that's what ChatGPT told me
😂😂😂
Bro where the hell were you all these years... I graduated then CZcams started recommending you. What a f*cking life
You didn’t think to search it?
Honstly kind of sounded like my life, but hey I'm also kinda also just riding on everything perfectly and missing everything at the same time... XD
Same 🥺
Same 😣
This is one of those questions that it's intuitive as hell to answer.
Great explanation! Now looks easy! :)
it’s one of those questions that seems hard when you look at it but are extremely easy when you do it
It’s also one of those questions that you will NEVER EVER run across, outside the classroom, in this thing we call LIFE!!! 😂😂😂💯💯💯
didn't seem hard when I looked at it.
it had to be a power of two and 8 was too low so... 256
The way he answerd was wrong
Fr
@@DFWJon you're literally living in world explained by math
My procrastination knows no bounds, I’ll end up studying Astro physics before I finish my course
Got a fluids exam tommorow and idk what I'm doing here
@@shaykirby5910rlly learn Reynolds transport theorem that shit will carry you
No bounds? How will you solve for your unknowns?
@@Cobalt_11 we had midterm 1 it was about hydrostatic forces mostly, but I'll keep that in mind!!
On a positive note. At least you are not wasting time watching other things like random animal videos
I remember this exact question in some point during my childhood.
Shoutouts to 2048 for helping me stay fresh on my powers of two
My CS Degree taught me that it has to be 256 without needing to calculate anything
That the number you know because you have been taught but a person who is doing it for first tim need to do this process and also it's a proof that 256 is tha answer
Yes bro
@@riksarkar4343 not really, with just guessing and logic its quite easy to get the answer. A and B is too small, C is not in the 2^x (like 2, 4, 8, 16, etc.) and E is just absurd
@@zwatchxd9175 no wonder maths was grounded from logic hehe
@@riksarkar4343 not really, D is the only logical answer
For me, seeing that 2048 is 2 to the 11th power and then seeing the relations between the number 256 and 2048 was enough to confidently say that D was the correct answer.
Pshh E is clear correct answer
Nerd
@@TheKinglyWay "nerd" 🤓
@@TheKinglyWaycool nerd
The ans is A…idk what everyone is talking abt
😆
Wish I had him as my tutor during highschool
no you don't
Meanwhile The kindergarten kids in China and India be like: give us tough problems.
Exactly, this is too easy
@@FullmoonFoxx I was talking about math skill and not government's policy making....poverty elimination doesn't depend on individual skill alone....whereas individual skill is personal....and it is precisely to escape poverty many students work extra hard to excel at math and science in India....and many have escaped poverty as a result.
This question isn't hard at all. It can't be 0 or 69420 obviously, so it must be 40 or 256, and considering 256 is a power of two, it's pretty clear what the answer is
Don’t forget Asia aswell.
@@army_x7849 bruh India and china are in Asia
you could also do this by deducing that 0^0 is 1, 8^8 would be way too small, 40^40 and 69420^69420 (69420 would be too large aswell) don't have anything to do with a power of 2 so the only thing left is 256^256
40 and 69420 are multiple of 5 so easy cross out. 8^8 isn't that large considering 2^1024. So easy win
0⁰ is not 1 lol
@@ThatisnotHair does it matter? it would be either 1 or 0 so either way the result would be too small. Since it's undefined it isn't the correct answer
@@ThatisnotHair it is
Anything to the power of 0 is 1
What dumbass countries have multiple choice maths tests anyway, they should just give you a box below the question for your work.
Borat: "Very nice."
Nice way of solving!
I really appreciate the lessons on practical math.
" _I didn't solve it but what I thought was the correct option_ "
Two of the answers involve a multiple of 10, which can only be created by multiplying 2 and 5.
We are only ever multiplying by 2 on the right side (2^x = 2•2•2•...), precluding those two options.
2^n≠0, when n is an integer, leaving only 8 and 256.
8^8 = (2^3)^8 = 2^24
256 is the only remaining option.
I always loved these kind of "work smarter, not harder" answers in math !
This guy is going to be so excited when he joins the working world and learns about matlab
Me: CS major, it’s 256 immediately lol
😂 those numbers look so familiar.
yeah its pretty ez. the right hand side is a power of 2 which is the only prime here. so the left hand must be a power of 2 the only number here is 256
@@khaledchatah3425 But by that logic 8 is also a power of two.
Me: a regular guy, there's no fucking way 40^40 is that big so it must be 256
@@anamikadey09 yeah true. u can see immediately that 8 won't work since 8=2^3 u have only 2 options. Should have added that
Me, being a software developer: yeah it's 256.
I tutor some kids in coding. I’m going to hand this them and see which one of them realizes it’s four lines with a DO-LOOP UNTIL
Keep it up love this
Great explanation.
I instantly started crying when you started going down the list. I was like “WHERE DID HE GET THOSE BUMBERS FROM”
Bumbers
He divided the numbers by 2 to get its half.
@@yassarwar9161 Oh Thxs i now understand how he got that number. I would have just but E
what is a bumber
Never solve a question in a straight way use the options
- Wise Man
Subscribe to my channel for more videos on Math
good thing this only works so good with exacxtly these numbers
India's JEE ASPIRANTS laughing 😂 in this easy peasy also I am laughing now 😂😂😂😂
I honestly just put natural log on both sides and do the lambert W function, never knew ur solution is unique and easier💀💀
Yea we didn't do these types of questions yet NOR the Lambert whatever thingy function u are talking about
Such questions can be solved easily by logarithm
It would be easier if an inequality was mentioned
So we would just use Jensen inequality
Piece of cake ques
@@epikherolol8189 I mean usually when I see x^x complicated equation my first initial thought was just put ln(x) in both sides and work my way to make it as x*e^x so I can put the Lambert W function
@@sicko5821 what is the Lambert function tho??
I understood the natural log on both sides but what is Lambert function??
@@epikherolol8189 it is an inverse function for x*e^x, it is also called the product log
Bprp made a good vid about it
This is definitely not the kind of problem you’d ever see as a multiple choice problem
You do see this type in A-levels or K12 Math but yep the options are SO badly chosen in the first place it’s a no-brainer
I’m not even in school anymore but I’m still saving this for later
Thanks for sharing Man !
Math is actually really cool. Too bad teachers aren’t teaching it that way.
You would like them to teach power of a power this way? Lol
Please watch nv sir lectures.. his teaching will meet your expectations
Who are you to comment on the way teachers teach their lessons?
@@firehalf2935 its not about how teachers teach, its about if they even teach. At my school most of the teachers don't try at all and I have to rely on the internet and textbooks to teach me most of the material.
@@kaisiclelmao maybe talk to your classmates who annoy, berate and humiliate your teacher daily. Then they might not hate their jobs everyday 😂😂😂
I swear to god sometimes I think your trolling is and then I actually follow the math and it checks out.
This is honestly helpful. Im very slow and making stuff slower is helpful.
They always told me “when in doubt, c’s the route”. Nailed it again!
Check again
But it was D.
@@eoungbyul378 😂😂😂😂
Wait till this guy learns about logs.
Omg 69,420. Legendary math teacher right there😂
I really really really like these 60 second math things dude ty
I love this stuff
It looks scary at first, but your explanation makes it easier to digest and eventually not scary at all.
dude this was easier than the things we were taught 8th grade
Except it wasn't though and you're a child grossly overestimating their intelligence
@@wavingbuddy3535 It is easy bruh. Just eliminate the options. There's no way it would be A,B or E, that leaves only C&D. 40 to the power anything will always have an unit digit with 0 but 2 to the power anything can never be zero. That just leaves option D and that is correct.
Damn that's way easier than my "eenie meanie miny mo" method
Literally math teachers saying that formula is needed
I knew it would be much faster simply plugging in all the answers until it was right, but I found it much more satisfying to generalize the solution mathematically rather than simply guess. I started with a system of equations:
x^x=(2^a)^b where ab=2048 and 2^a=b
The end solution here would of course be "b", and "a" is some unknown introduced with the intent to be solved out. Knowing 2048 is 2^11, putting "a" in an assumed form of 2^c you can work through it to form
2^(2^c+c)=2^11
which simplifies to 2^c+c=11, and you can easily see that c=3. Plugging all the way back up you get a=8 and b=2^a=2^8=256
A much better answer than the video!
Multiple choice would just lead me immediately to the 256 because the other options are either not powers of two or too small in the case of 8
You’re a fool, it’s clearly 69,420😮
gg xD
By option👍😊
The "show your work" bs math teachers put you through.
I remember taking the SAT and not knowing any of the math.
So I just reverse engineered the problems using the options given and figured out how to do it that way.
Then, when I started classes, they put me right into algebra 2. But in reality, I needed to be in pre-algebra cuz I never learned it before.
Still passed the class but I had to go to tutoring every day because I didn't know the basic shit.
Lol "reverse engineered".
You… you took the SAT without taking algebra 2? What the hell is wrong with the American education system.
Passed my highschool psychics and some chemistry, by using reversed calculation, but wasn't multiple choices, I used the notations and knowing the relations, I knew how to get the formulas to calculate the process and get the answers! I don't like to memorize every different formulas, only memorized the main formulas which can derive into others 🤧😆 and I was one of the few who passed the tests without retaking ( 7 people out of 26 students at that time if my memory isn't trolling me 🤷😂)
@@bolson42 I took the SAT halfway through calculus
What course youre taking depends on your skill and you can take the SAT at any age
@@pearlsswine What's the problem with that?
I learned more from CZcams than I ever did from school, this is the proof.
School has limited time to teach you these concepts. Compared to hundreds of youtubers who have a whole life time to teach these concepts.
@@anthonyJones-ll4eiCouldn't agree more, I just felt like school is just draining my time instead of teaching me (ngl sometimes I don't even had enough time to study in the library)
It's because you pay more attention on youtube than you do in school. It's no one's fault but yours
@@Burningarrow7bros baldis basics 💀
You dont pay attention in school
Great❤
That's a very brute force approach with low certainty to provide the right answer. Still, whatever works. 👏🏾👏🏾
I love the 69420 reference 😂
@@J0DanEli You say that like you think that's going to do anything 😂
@@J0DanEli Well, the creator thinks it’s funny
The best solution is to just look at the answers and pick the only one that makes sense lol
that’s cool BUT process of elimination works like a charm with this one 😭
You write "4" really unique way..
2048 * ln(2) must be around 256 * ln(256). That's how I did it
Yeah , same , I use ln and exp
Indeed,ln(256) = 8ln(2)
It can easily be done by considering the unit values of RHS and LHS
💯
Indian science student are laughing after seeing this question .kash aise questions jee advance me aa jate💀💀
Yes just find unit digit and options will help
Aint no way, computer science students can answer this in a split second
@@nothingSpecial5680as a student who just entered 11th pcm , I see this is an absolute win ❤
Option E was wild
I solved it within a blink of an eye
Bro they knew what they were doing with that "sixty-nine, four-twenty"
You can just use each answer on the multiple choice to find the answer with even less work. Obviously this is an easy out
That’s my favorite tactic: guess and check. (Except he’s not really guessing.)
The mighty power of multiple choice
this man gives me more knowledge than my math teacher
for any
x^x = z
equation,
x = e^W_k(log z)
or equivalently
x = e^W_k(ln |z| + i(θ + 2nπ),
and for any
x^x = 2^b
equation,
x = e^W_k(b/log 2)
or equivalently
x = e^W_k(b/(ln 2 + 2nπi))
where W_k is any branch of the Lambert W function/product log and n is any integer, and θ is the argument/angle of the possibly complex number z or b, this means there are not only infinite possible values due to infinitely many multiples of 2πi, but also due to the infinitely many branches of the product log, also it's pretty rare to find an equation of that type with an integer solution. Note that you have a real solution to the equation only for any b/log 2 greater than or equal to -1/e.
the way you solved the equation though, that's not how you solve equations and if it were different by one unit the method wouldn't hold
…or just plug in the options until something works
That's a really long and hard to understand way of saying what I came here to say, it wouldn't work with one number higher or lower, nice job
Yeah, just like that.... and I wonder why I struggled
Only time playing an online game ever helped me see a solution that quickly
I'm an engineering graduate and we deal with maths pretty much everywhere and I can confirm you i would answer 69420 without even a second thought
Did you fail your math class or something.
@@skyral4137 its 69420 bro
Indian 8 class students: laughing in the corner
@@interiorbrainiac2705 but they do know this
@@gitanjalidas8190 no bro
@@gitanjalidas8190 they don't know these sequences
I'm in 9th this was easy but never thought in school
Thanks for this 👍
yes show more i need more
The most useful yt shorts for me thx
It's nice cause it shows the way how you'd solve it, but in a test, you basically wouldn't get all that time, so you go by elimination game, where it will just take you a couple of seconds really.
0 and 69420 are out just by looking. 40 is also out as we are only dealing with 2's here. 8 is too small. So that leaves us with 256.
Just look at the option and use elimination rather solving, didn't even took a sec😂
this video is about the process not the actual answer
Hey man, i was talking about taking math as a hobby once again and youve been helping me out, thank you!
You're very cool man!
As an asian student, i can finish it just by a look
Same here😂
Same here lol
Then why i dont....😮🤔🤔☹️☹️
I haven’t loved learning math since I got out of high school. Thanks for teaching me something new and something I enjoyed
Damn it!! I just needed to know this just the other day!!!
This was such a cool solution
My man just spittin middle school math
Your videos are really helpful for my CSAT exams.. Thank you so much.. ❤
this shit blew my mind awesome stuff i want more
dang those Mr Bean math videos Made my recommendation full of math problems
Türkiye sistemindeki soruların yanında melek melekk
Soruya 5 saniyede bakıp çözdüm lan. İnsanlar artık buna nasıl zor diyorsa.
Anyone who has ever assembled a computer points to the only logical answer without calculating
Logic, get you through 🎉
You have literally taught me more math than my whole educational experience
Man it's such an easy question, just need to know 2^x seq and check the option