Can You Pass Harvard University Math Exam?
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- เผยแพร่เมื่อ 7 ก.พ. 2025
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@higher_mathematics
#maths #math
X=3. It's mental arithmetic
what about it if you were to ask the solution on paper without the use of comparing?
Thats the reason why u are not in Harvard
@@99eigencharu see havard needs solution to the problem too😉
Just put x = 3 by hit and trial method!
My advice as a 10th grader.
Certified chtya 😂😂 , beta vo Harvard h . Tumhare IIT se 1000x better . Sorry , tumhare 10th ke 🤡 result se 1000000x better.
Oh thats so smart .......bro if u get a question to prove that it is a triangle just for example will you say the same thing there also?? Or will you prove it
@@PriyanshuSharma-z5zHarvard question is mcq type so you don't have to prove:)
nah nah nah if the Value of x Is 3 thn the Equation should look like this - 3x3 +3 = 30
or solve it 9+3=30
No sense
@@CHEEKU_GAMER123 le me guess you are just a 7th grade student right?.......in equation its 3 to the power x not 3*x
ok but 3^x=x=30 => 3^x+x=27+3 => 3^x+x=3^3+3 ==> x=3 easy
3ˣ+3=3³+3
3ˣ+3=3³+3
-3 -3
..................
3ˣ = 3³
ln3ˣ = ln3³
x ln3 = 3 ln3
x ln3 = 3 ln3
--- ---
ln3 ln3
x = 3
Knowing is not the same as proving.
Fake
Everything this channel does seems to be about lambda-W function. We need a little more variety please.
@@Taozilin yes but you need to do it in the "hard" way or else the test graders in Harvard won't take you srsly.
A nice exponential equation.
3^x + x = 30
To solve for x, we'll need to use numerical methods or approximations, as this equation doesn't have a simple closed-form solution.
Here are a few approaches:
*Method 1: Trial and Error*
Try different values of x to find the solution:
x = 3: 3^3 + 3 = 30 (matches)
So, x ≈ 3.
*Method 2: Graphical Method*
Plot the functions y = 3^x and y = 30 - x.
The intersection point will give us the approximate value of x.
x ≈ 3.
*Method 3: Numerical Methods*
Use numerical methods like Newton-Raphson or Bisection to find the root.
x ≈ 3.
*Verification*
Substitute x = 3 into the original equation:
3^3 + 3 = 27 + 3 = 30
Verified!
The solution is:
x ≈ 3
Please note that this equation may have multiple solutions or complex roots, but x ≈ 3 is the real solution
1) If x < 0 then 30 = (1/3)^|x| - |x| < (1/3)^|x| < 30 : contradiction, so there is no negative solution.
2) x=0 is not a solution
3) f(x) = 3^x +x - 30 increases strictly in (0,+ infinity), so f has at most one zero (i.e. there is at most one solution)
4) x = 3 is a solution.
Conclusion : 3 is the only solution of the equation in R.
7 class students solving it in mind
Got it in seconds 😂
nah nah nah if the Value of x Is 3 thn the Equation should look like this - 3x3 +3 = 30
or solve it 9+3=30
No sense
@@CHEEKU_GAMER123 bro it isn't (3x3) its (3³) => 3 × 3 × 3 = 27
27 + 3 = 30
@@SaquariusGaming My bad I didn't saw it was power
Just do trial and error method
A beautiful and very clear explanation.
Some of the commenters are silly passing themselves off as genii. It is the method that counts not the simple solutions, or trial and error, or solving by spotting the 3 factor.
The poster is passing the question off as a Harvard University math exam. It's the same misrepresentation every day. Why you would call out TH-cam browsers who happen to state that they can see a real root, is beyond me. Why do you hold them to a standard of mathematical prowess, when they require none? It seems stranger still that you don't hold the poster to a standard of intellectual integrity, while they bait views with false claims.
@@davidnewell3232its the concept that matters to me personally, even though i solved it from the thumbnail, i was puzzled on how you would solve it normally with theory
Will you solve it using the full method that he has shown during a competitive examination….i don’t think so….this is just a foolish solution from the point of view of competitive where you don’t have the need to show the working…but in some subjective paper this would be the appropriate solution!!
@@riddhimanagarwal07 OK, then!
I was struggling with this for a while; then I put the video on, and after hearing the step “divide by 3^x” it finally clicked, and I was able to solve it from then on. Great video and explanation as always.
I'm by no means a math genius, but it was explained so well that even I understood the solution, thanks, you saved an otherwise boring evening for me (it's now evening in Germany)
Sadly he cheated! (an der Stelle, wo er 3^30 in 3^27 * 3^3 aufgeteilt hat und die Lösung selbst für den Beweis genutzt hat! In etwa wegen 3^(3^x+x) = 3^30, wenn man weiß, daß x=3).
At 10 min, rewriting 3^30 as 27×3^27 is equivalent to guessing the answer to 3^x = 30-x, which is guessing the answer to the original question. This is like giving a complicated procedure for fixing a car where step 10 is "take it to a mechanic".
I do enjoy your videos, though. Your voice is very relaxing.
Uhm... I just wrote a comment saying exactly that. And then I read yours. You were first. You are right. He only can factor out 3^3 * ln 3 * 3^27 if he KNOWS 30-x = 27. And you don't need the Lambert function at all. Actualle he does not even use it to calculate the value for W().
@@jlinkels Then I suppose, I'm at least third. I called it "proof by confusion"...
@@jlinkels "And you don't need the Lambert function at all." Here I disagree. It's straight forward: If he looks up W(3^30 ln3), he'll get 27 ln3. Then x = (30 ln3 - 27 ln3) / ln3 = 30 - 27 = 3. But that's not what he did!
3 is a trap, guys. The point is, why should it be 3 and not something else, especially when you have no intuition?
A monotonic function or something like that might exclude other possibilities once you have 3 as the answer, but you arrived at 3 based on intuition.
Your pfp checks out with this comment of yours
Tell me other possibilities
So what exactly are the other possibilities...?
Another guy in this comment section made this a valid guess:
He said "x = 3 is a solution" and he could prove, that there is
at most 1 solution (strictly monotonic function from -inf to +inf). That's all you need!
Super elegant and interesting solution using w function.
I solved it with only seeing the thumbnail and the video is 14 minutes 😂
Me too bro
idem
8 vi class ka h squares & cubes aana chahiye
Same 😂
Me tooo 😂😂😂😂😂☺️
Ans 3 as
Atp
3^x + x = 30
3^x + x = 27 + 3
3^x + x = 3^3 + 3
So,x=3
Your are genius
Nice way to prove this equation
I know this easy to solve but hard to prove
And you can do it
Lets break 30
27+3 = 3'x +x
3*3*3+3 =3'x +x
3'3 + 3 = 3'x + x
x= 3
Why giving a simple answer when the complicated one is so beautiful.
Answer is 3 , I didn't even watch the vid or comments
Calculated by seeing the thumbnail 💀
I guess it's x=7.5
To solve the equation , you can combine like terms:
1. Combine and :
4x = 30
2. Divide both sides by 4 to isolate :
x = \frac{30}{4} = 7.5
So, the solution is .
X=7.5
Are you dumb
I think a more helpful way to present this method would be to show the given equation, demonstrate how easy it is to figure out, then mess it up with numbers that don't solve easily. What do we do now?
Thus we would need a generalized approach to problems like this. In to save the day is the Lambert W function.
f(x)=3^x+x is monotone and increasing. Hence, the graphs of f(x)=3^x+x and y=30 intersect once. An obvious solution is x=3. There are no other solutions in real numbers.
I was funding such a math . THANK 🎉YOU SO MUCH.
Also differentiate it is monotonic hence only x=3 satisfies
As being Indian we put x = 3 by hit and trial and get answer in few second
I swear some algebra problems I can do in my head since 4th grade but explaining it was something I couldn’t do whatsoever
Given that you explain the simplest algebraic manipulations, I think the step where you transform W(27 ln 3 · e ^ (27 ln 3)) = 27 ln 3 could have used a little explanation. (It's because the Lambert W is the inverse of the function in the brackets, by definition).
This is proof by confusion: A long complicated calculation, with a special kind of trick in the middle.
When you split 3^30 = 3^3 * 3^27, you've implicitly used your knowledge about the solution itself! (27 + 3 = 30).
Not straight forward! That would be (30 - x) ln3 = W(3^30 ln3) => x = 30 - W(3^30 ln3) / ln3.
Look it up and get W(3^30 ln3) = 27 ln3 => x = 30 - 27 = 3.
since 3^x+x is a strictly monotonous function and x=3 is a solution, it is the only one.
В левой части - монотонно возрастающая функция,в правой - константа. Следовательно, уравнение имеет не более одного корня . Очевидно,что х=3 - корень. Вот и всё.
While it IS true that you use the Lambert W functions to solve equations of this form, that is not how it is done here. Actually you don't need the Lambert function at all. Because he does not ever calculate the value for W_0(x). He only puts the Lambert function on both sides of the equal sign to show that W(p) = W(q). At 09:42 he shows that 3^30 * ln3 = 3^3 * 3^27 ln 3. So how does he know that? Why not 3^4 * 3 * 26 ln 3. You can ONLY do this when you know what to expect, namely 30-x = 27. And that is exactly the same as guessing that x=3. And you totally DO NOT need that Lambert function to come to this. Although it is a nice way to simplify the derivation. You just have to skip the step that W(x*e^x) = x. Since you do that on both side of the equal sign you might as well omit it.
I don’t think it’s based on knowing 30 - x = 27.
Example, if I saw W(4^260 x ln4), then I would think about different exponents of 4 to rework the expression. Since 4^4 = 256, this could be rewritten as W(4^4 x 4^256 x ln4) or W(256ln4 x 4^256). Following the additional steps will then make it possible to solve Lambert W.
If I take x= 3 and put in this equation then
X=3
3³ + 3 = 30
27 = 30 - 3
27 = 27
L.h.s= r.h.s
Then the value of x is 3
From where did you get x=3
You can't take it by your own will
3 satisfies the equation and graph of 3^x and 30-x meets at only one point. Easy
Its really great that you explained all the steps and did it correctly, bravo 🎉👏
But I guess trial n error method works best for MCQ's 😉
- advice from 8th grader
At a quick glance 3^3 = 27 then 27 + 3 = 30 and x = 3.
3 works which is nice for a times test, but the Algebra was "good fun" & math practice...
the real thing is proving the equation. therefore this video is really helpful and btw those who are saying i solved it in my head, I know its easy but the real thing is proving and showing how.
This question is not about just puttin 3 and get answer but to learn a new approach to this problem
I was able to do this in mind
Obviously, x=3 is solution, but ,if x 3^x+3>30
I'm from "Old School" learning, and simple expressions like this should be first looked by trying solutions of 0, 1, 2 or 3.
And guess what --- 3 works.
This Lambert function is very useful.
You set a function f(x) = 3^x + x it is 1-1 and x=3 is the only solution
USA's question : 😂
India's JEE AVD : 💀
just take x common and break 30 = 3*10, from observations x =3. If you dont believe then simply put value of x in the equation you made by taking x common and you will get 30
But:
3x/3x = 30-x/3x
1 = 30-x/3x
3x = 30-x
4x = 30
x = 30/4 or 7.5
Its too long you can just put value by guessing and get the answer tho😂
X=3 because 3^x+x=30
Then (3)^3+3
=27+3
=30
3^x+x = 30
3^x+x = 27+3
3^x+x= 3³+3
X= 3
Bro I did this in like 10 seconds just looking at the thumbnail, I guess I deserve to be in harvard
It was way too easier by hit and trial 😕
As 30 is a small no. we can easily calculate value by putting random value to this
x=3
I solved it by seeing the thumbnail in 2 minutes even though I haven't touched algebra in yrs since I took humanities
3³=27
X= 27-30=3
foolish how many people think they are smart just because they can see the answer is 3. The instructor has taken a simple problem in order to concentrate on explaining the process. He could have chosen numbers where it would have been very difficult to determine the answer by inspection but this would not have helped explaining the process. However, I am not comfortable with the solution of the right hand side of the equation ... minute 10 ..... because I cannot see how you knew to do this. Furthermore, I suspect that this double Lambert W solution will only work with conveniently chosen numbers and not as a general proposition. Therefore rather than continuing to the explanation of the process, I think applying W to the right hand side, while interesting, is really off the subject.. in any event a very good video with a good explanation...
X=3, it takes me three seconds to solve it .😂
The video title should be - How to make a simple solution unnecessarily complicated.
Let, x = 3
LHS,
3^x + x
-> 3^3 + 3
-> 27 + 3
-> 30
= RHS proved
Hence x = 3
Thats how we deal with such questions in competitive exams in India
Jee advanced teaches you to think fast but not proper mathematical induction
3^x +x = 30.
3^x+x = 27+3
3^x+x=3^3+3
LHS and RHS equal.
So, x=3.
Btw, i calculated in mind by just substitituting 3 directly and instantly lol😂
Even Stephen Hawking's soul will cry after seeing your solutions. 🤣
Looking at the oength of the video, I was hoping it will have imaginary solution but all this was to get 3 😭
Good,if they need the solution to the question,but this can be done easily without that many steps
Me before the video: this better not be another Lambert W function
Me right in 3 minutes: of course
Who are successfully calculate this answer in brain 🔥👽💫🙌
I solved it in my mind under 20 seconds 😂
Uni math, I solved it in my head in 5 seconds, and I am one of the slowest students in my math class
Bruh it took me less than 10 seconds to work out that it is 3 in my head
But if we differentiate the expression, we get x=-log base 3(-ln(3)) now how do prove that this equals to 3
Simple exponential arithmetical Sum
And linear equation
x is 3. Took just half a second
X=3 simple just by seeing
Very nice, however - you didn't really applied W function. I mean - you didn't really compute it, nor read from tables. Only to compare both sides.
So it should be possible to solve with another compare trick.
3^x + x = 30
x=3 simple
3, by inspection.
Easier method:
Step 1:3^x=30-x
Step 2:log 3^x=log(30-x)
Step 3:xlog3=log30/logx
Step 4:xlogx=log(30-3)
Step 5:xlogx=log27
Step 6:xlogx=log 3³
Step 7:xlogx=3log3
By comparison
X=3
I am in grade 12 cbse
Even easier method
3ⁿ+n=30
3ⁿ=30-n
3x3x3=30-3
N is 3
Wait how did you get to step 4 from step 3?
i was teaching calculus to the engineering students integrations, derivations, differential equations, (and solvings) laplace and frouier transformations, rotation gradient nabla operators, etc.. many years ago (more than 45y .But now i cant remember W function right now..Can you explain breafly?
That was the same thing I thought. I am not teacher, only a graduated engineer. In 1983. Never heard of the "Lumber double the function" . It seems to be Lambert W function. Which I think is somewhat far fetched for this solution. But then I again I am no Harvard student.
Very nice, very clever. 👍
it's easy to solve by graph , then by hit and trial x= 3
but what about 3^x-x=30
please solve it too
When 1 marker comes for 5 marks 😂
Trueeeee😂😂😂😂
There must be an easier way. I also wonder if this was the way Harvard intended it. I agree that inspection does not show why.
Because students think it has some hard calculus question but it just some simple question
3^x=x=30 => 3^x+x=27+3 => 3^x+x=3^3+3 ==> x=3 easy
@@andregomes554 no some times x can be in decimel,irrational and imaginary
Easier method:
Step 1:3^x=30-x
Step 2:log 3^x=log(30-x)
Step 3:xlog3=log30/logx
Step 4:xlogx=log(30-3)
Step 5:xlogx=log27
Step 6:xlogx=log 3³
Step 7:xlogx=3log3
By comparison
X=3
I am in grade 12 cbse
@@mohitraj4377 wrong log(a-b) is not equal to loga/logb from step 2 to step 3
Im 5th grade and i did it in 15 seconds, I don't believe its really a Harvard question
Thats very easy...i challenge anyone here to try JEE Advanced Question
It's 3
Wow so easy i am class 7 solving it orally. Ans is 3
this is the reason why I use trial and error😅
X =3 very easy for indian
3^x + x = 30
X= 3
No math this is just how I guess it
Ye, in one step. X = 3.
This is quite easy for me being a seventh grader
Ok, this university question is noting in comparison to a grade 12 IIT-JEE question.
I guess I can take admission now
3 is the answer
i am shocked that as a student in grade 4 (im using my moms account) i can already guess the answer mentally and dont have to do all of that long equations
X=3 clearly by observing 😅
11year olds Me:*thinking for 1 second*
My mouth: it's 3 easy😂😂
Welcome to Lower Mathematics youtube channel 😂😂
Indian Mathematics Solos ☠️☠️☠️☠️☠️
bro speaks in one breath
IT JUST LIKE I THINK X IS 3 3^3=27+3=30
Please make a video solving 2 power x + x = 5
3^3 + 3 = 30