Hardest Exponential Equation!

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  • เผยแพร่เมื่อ 23 ธ.ค. 2024

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  • @Vega1447
    @Vega1447 หลายเดือนก่อน +1138

    There is no Harvard entrance exam.

    • @kabulykos
      @kabulykos หลายเดือนก่อน +177

      It's really annoying how correcting misinformation on a site like this always causes its Algorithm to promote the misinformation more than your correction

    • @kaliss6110
      @kaliss6110 หลายเดือนก่อน +51

      its called clickbait

    • @mightyoak11111
      @mightyoak11111 28 วันที่ผ่านมา +2

      I thought to get accepted to Harvard one has to simply express support for hamas or any other jihadist terror group. 😂😢

    • @thadwuj668
      @thadwuj668 23 วันที่ผ่านมา +7

      I bet the video creator pulled this from a qualifying exam and has no concept of what a QE even is...

    • @thovenach
      @thovenach 19 วันที่ผ่านมา +4

      There is no vega1447

  • @robertanderson1043
    @robertanderson1043 28 วันที่ผ่านมา +341

    I define the Skibbity Q function as returning x when applied to x^x. Therefore the answer is Q(25).

    • @brain_station_videos
      @brain_station_videos  28 วันที่ผ่านมา +29

      Lambert W is fr 🥲

    • @robertanderson1043
      @robertanderson1043 27 วันที่ผ่านมา +61

      @@brain_station_videos Lambert W and Skibbity Q are both equally real.

    • @WilliamGerot
      @WilliamGerot 27 วันที่ผ่านมา +8

      x^x has too many discontinuities and is unable to be broken into branches as the Lambert-W function is.

    • @Nethuja_GunawardaneSL
      @Nethuja_GunawardaneSL 26 วันที่ผ่านมา +3

      @robertanderson1043 I already made that function long ago and named it the mu function μ(x). So it's mine, not yours.

    • @budderman3rd
      @budderman3rd 25 วันที่ผ่านมา

      ​@@robertanderson1043Give me your rigorous definition and details of it. If not, get tf out.

  • @williamstraub3844
    @williamstraub3844 หลายเดือนก่อน +465

    This is why I hate the Lambert W function! It's like saying "What is the solution to x = sin(37)? Why, it's arcsin(x) = 37." The W function is useless unless you have a calculator or Wolfram Alpha handy.

    • @brain_station_videos
      @brain_station_videos  หลายเดือนก่อน +56

      That's true. But atleast we are able to find a numerical value.

    • @0943kt
      @0943kt หลายเดือนก่อน +8

      i think you can write your answer as an expression with a function

    • @adw1z
      @adw1z หลายเดือนก่อน +26

      I'm guessing you hate logs and exponentials and regular sines/cosines/tangents and square roots and reciprocals too then?

    • @JeanG-s9j
      @JeanG-s9j หลายเดือนก่อน +35

      I agree, its like if I could create my own function, lets say J(x^x)=x, then if x^x=25, the solution is x=J(25).

    • @TheMathManProfundities
      @TheMathManProfundities หลายเดือนก่อน +5

      ​@@JeanG-s9jBut you wouldn't be able to get a value from that. It's more like x=√2. It had a value but you basically need computation to evaluate it to any significant level.

  • @user-ix9zu5es6j
    @user-ix9zu5es6j 28 วันที่ผ่านมา +70

    1:20 sports

    • @math_solver_N
      @math_solver_N 23 วันที่ผ่านมา +4

      EA sports to the game

    • @tunistick8044
      @tunistick8044 19 วันที่ผ่านมา

      AHAHAHAHAHAHAHA

    • @7F0X7
      @7F0X7 18 วันที่ผ่านมา

      what kind of mind do you have. You *MADE ME HEAR THOSE WORDS WITH THE EA ANNOUNCER'S VOICE, DANG IT!!!* @.@

    • @Krazykahaan
      @Krazykahaan 16 วันที่ผ่านมา

      Nah, the guy def did it on purppse

  • @SVMNSP6213YT
    @SVMNSP6213YT 2 หลายเดือนก่อน +406

    i think it isnt log? the natural log(base e) is ln(x)

    • @3141minecraft
      @3141minecraft 2 หลายเดือนก่อน +41

      You are right. log is base 10 logarithm and ln is the natural logarithm(the base e logarithn)

    • @shlok2444
      @shlok2444 2 หลายเดือนก่อน +10

      I guess the solution is just to replace log be ln

    • @t-cc3377
      @t-cc3377 2 หลายเดือนก่อน +9

      It was a notation error. At least the narrator said "the natural log".

    • @MD-kv9zo
      @MD-kv9zo หลายเดือนก่อน +7

      Apparently a lot of people(including my maths and physics teachers)do that even though it just gets more confusing. Log should be to the base 10 and ln to the base e.

    • @FundamSrijan
      @FundamSrijan หลายเดือนก่อน +7

      ​@@t-cc3377jfnot error , difference .
      It's still heavily used for natural log in many places .

  • @KasyapH
    @KasyapH หลายเดือนก่อน +46

    3:43How do you calculate this?

    • @1-human
      @1-human หลายเดือนก่อน +4

      using numerical methods

    • @DrHyperionSun
      @DrHyperionSun 26 วันที่ผ่านมา

      I would try Newton's method assuming z=W(ln(25)) and Derivating f(z).
      But this is because I am dumb, sure there are more pretty methods.

    • @latorredelreloj
      @latorredelreloj 25 วันที่ผ่านมา

      W is a lesser known function but it is well-known enough for many mathematical softwares to have it as a built-in function

    • @tunistick8044
      @tunistick8044 19 วันที่ผ่านมา

      Newton's method

    • @jaudatalhusen9049
      @jaudatalhusen9049 13 วันที่ผ่านมา

      ​@@DrHyperionSundisliked for low self esteem

  • @tsolanoff
    @tsolanoff หลายเดือนก่อน +18

    It’s a bit confusing to require applicants to know advanced math (Lambert W function)which is supposed to be taught in higher education institutions

  • @axumitedessalegn3549
    @axumitedessalegn3549 22 วันที่ผ่านมา +12

    A better answer is 2.9632 and you can just do log(25)/log(x) in a graphing calculator and look for a value that is x=y

  • @divyamkumar1339
    @divyamkumar1339 หลายเดือนก่อน +51

    Can you please write ln(x) instead of log(x)? Natural log is not the same as log with base 10.

    • @CAustin582
      @CAustin582 28 วันที่ผ่านมา +3

      In American academia, log is implied as being base e unless otherwise specified

    • @death704
      @death704 26 วันที่ผ่านมา +1

      In the whole of calculus, we rarely use log with something else as base except for e

    • @edwolt
      @edwolt 17 วันที่ผ่านมา

      ​@@death704In my calculus course, when talking about natural log we used ln.
      But for some reason, in CS courses people used just log as meaning log2 when they could've be using lb, which is kinda confusing.

  • @StevenTorrey
    @StevenTorrey 2 หลายเดือนก่อน +29

    This is the first time I have heard of the W Lambert Function. Though the procedure looks familiar.

  • @Zeddy27182
    @Zeddy27182 29 วันที่ผ่านมา +33

    The log(x) is not necessarily base 10. It depends on how it is defined!
    High school: base 10
    College Math: base e
    Python, R, etc : base e
    CS : base 2
    Even the definition of natural number varies:
    Math: 1, 2, 3, ...
    CS : 0, 1, 2, ...
    Overall, it really doesn't matter at all.
    "The essence of mathematics lies in its freedom." - Cantor

    • @cdmcfall
      @cdmcfall 28 วันที่ผ่านมา +4

      ISO 80000-2, which is supposed to be international notation standards, says this:
      logₐ _x_ => logarithm to the base _a_ of _x_ ; standard, unambiguous notation
      ln _x_ = logₑ _x_
      lg _x_ = log₁₀ _x_ => This was formally just log _x_
      lb _x_ = log₂ _x_
      log _x_ => This should only be used when the base does not need to be specified (most calculators treat it as log₁₀ _x_ while many apps, including Wolfram Alpha, treat it as ln _x_ )

    • @alexandreclergeaud4672
      @alexandreclergeaud4672 16 วันที่ผ่านมา

      log is base 10, ln is base e

    • @aurelianmasdrag2179
      @aurelianmasdrag2179 16 วันที่ผ่านมา

      0 is a natural number in maths

  • @pbierre
    @pbierre 29 วันที่ผ่านมา +26

    It's ~ 2.96322. There is a more modern, easier to understand approach based on successive approximation and iterative computation. All you need is a calculator with exponentiation function x^y.

    • @WilliamGerot
      @WilliamGerot 27 วันที่ผ่านมา +3

      Ah and we find the computer scientist/applied maths person in the group

    • @Brigadier_Beau
      @Brigadier_Beau 22 วันที่ผ่านมา

      I used estimation and managed to get that it would be close to but less than 2.965. I didn't feel like refining further.

    • @gergokarath5739
      @gergokarath5739 3 วันที่ผ่านมา

      Bruteforced in calculator 2,963219774895. It's pretty damn close :D

    • @pbierre
      @pbierre 3 วันที่ผ่านมา

      @@WilliamGerot Do I detect a hint of "us vs. them"?

    • @WilliamGerot
      @WilliamGerot 2 วันที่ผ่านมา

      @@pbierre Nah I just love the different approaches people take it adds positive diversity

  • @andrewy664
    @andrewy664 หลายเดือนก่อน +9

    Hello, 2 errors here: (1) you cannot just apply an arbitrary (in this case -- even undefined) function to both parts of an equation without proving than you don't lose any root and don't introduce any new root; (2) the same, when author applies exponential function to both sides of the equation (particularly, x=0 becomes a part of the domain after this operation).

    • @maddenbanh8033
      @maddenbanh8033 หลายเดือนก่อน +2

      I don't see the problem here, if he's only focusing on the reals then clearly he's only using the principal branch and secondly while you werent exactly clear, 0 was defined at the start

    • @Munnstery
      @Munnstery หลายเดือนก่อน +1

      Adding to the reply by madden.
      The lambert W function is defined. It was defined in this video and is taught at degree level.

    • @andrewy664
      @andrewy664 29 วันที่ผ่านมา

      > clearly he's only using the principal branch
      ​ @maddenbanh8033 , it is not a problem in this particular equation, but it may be a problem in another expression. I consider this video it to be an educational one, so as a newbie I'd like to to see a precise and systematic approach here, not just a green way. Moreover, a student may get a penalty for not mentioning those facts and possibly introducing inequivalence. And all my initial points relate to the real numbers set only.
      @benmunn7481, the function is of course defined by itself, but not in the scope of this task. I've studied dozens of higher math disciplines for over 5 years, but have never heard aout it, so it's hard to say it is widely used here and there. My nitpick was that for some functions it is OK to do so, but for another we may lose equivalence during the solution. E.g. if we use f(t) = 0 instead of Lambert W function, we will end up with the solution that x may be any real number which is, obviously, an error.

  • @chouch
    @chouch หลายเดือนก่อน +38

    ...or why you should not study maths at harvard, nor watch random videos that pretend to be of mathematical nature. What a waste of time.

    • @SachinGupta-h7y
      @SachinGupta-h7y 19 วันที่ผ่านมา

      Are you in Harvard💀

    • @aurelianmasdrag2179
      @aurelianmasdrag2179 16 วันที่ผ่านมา

      youre saying it like any random can get into harvard

    • @bakasteveuwu2822
      @bakasteveuwu2822 9 วันที่ผ่านมา

      I mean if you are studying this and don't understand something then this video is a great tutorial

  • @azizbronostiq2580
    @azizbronostiq2580 หลายเดือนก่อน +13

    2:15 AAAAAAAH YES ! x is totally equal to e^log(x)

    • @az3224
      @az3224 หลายเดือนก่อน

      Log(x) to the base e tells us what should be the power of e to get x
      For example log2 to the base e equals 0.30103 this means e raised to power 0.30103 is equal to 2
      Similarly log x to the base e is the power to which e is raised to get x
      Therefore x =e^logx
      Hope it helps you 🙂

    • @azizbronostiq2580
      @azizbronostiq2580 หลายเดือนก่อน +3

      @az3224 yeah but no. He should have written e as the base of the log and not only "log(x)" otherwise is completely falsz

    • @partial-m4n
      @partial-m4n หลายเดือนก่อน +1

      @@azizbronostiq2580 Some countries teach log instead of ln. (And it’s more satisfying to write)

    • @azizbronostiq2580
      @azizbronostiq2580 28 วันที่ผ่านมา

      @@partial-m4n yeah but it's still wrong

    • @partial-m4n
      @partial-m4n 28 วันที่ผ่านมา

      @@azizbronostiq2580 Not really wrong, advanced people use that

  • @JUGNUMEHROTRANEETASPIRANT
    @JUGNUMEHROTRANEETASPIRANT 29 วันที่ผ่านมา +15

    I solved it in my mind as follows : X ln{x}=ln[25] Or ==>
    e^ln{x} . ln{x} = 2ln[5]
    Therefore, x =e^W{2ln[5]}. [OBVIOUS WHY OR EXPLAINATION GIVEN IN THE VEDIO{about W function }]

    • @JUGNUMEHROTRANEETASPIRANT
      @JUGNUMEHROTRANEETASPIRANT 29 วันที่ผ่านมา +2

      If one knows about W , it shall take him/her less than 1 min to solve it mentally , otherwise , one would make guesses{e.g here , x~3 is a guess}

    • @Nihalshanu22
      @Nihalshanu22 27 วันที่ผ่านมา +3

      @@JUGNUMEHROTRANEETASPIRANToh genius over here

    • @JUGNUMEHROTRANEETASPIRANT
      @JUGNUMEHROTRANEETASPIRANT 26 วันที่ผ่านมา +1

      @@Nihalshanu22 Thanks 😁

  • @donsimon2830
    @donsimon2830 หลายเดือนก่อน +10

    Q: What's green and commutes
    A: An abelian grape

  • @DeepakKumar-fi4gp
    @DeepakKumar-fi4gp 14 วันที่ผ่านมา

    To solve the equation , let us proceed step-by-step:
    Step 1: Rewrite the equation
    We have:
    x^x = 25
    \ln(x^x) = \ln(25)
    Using the logarithmic property , this becomes:
    x \ln(x) = \ln(25)
    Step 2: Approximation or numerical method
    The equation does not have a closed-form solution and must be solved numerically. Let's proceed:
    , so the equation becomes:
    x \ln(x) = 3.2189
    Step 3: Estimate the solution
    Try values for :
    If , (too large).
    If , (close to 3.2189).
    The solution is slightly above .
    Step 4: Refine using numerical methods
    Using numerical tools (like Newton's method), we find:
    x \approx 2.559
    Final Answer:
    x \approx 2.559

  • @thecompliationvideos4246
    @thecompliationvideos4246 6 วันที่ผ่านมา +1

    -Newton-Raphson method
    -formula: xₙ₊₁ = xₙ - f(xₙ) / f'(xₙ)
    -Initial guess: x₀ = 3
    1. f(3) = 3ˣ - 25 ≈ 2
    f'(3) = 3ˣ (ln(3) + 1) ≈ 56.66
    x₁ = 3 - (2 / 56.66) ≈ 2.9647
    2. f(2.9647) = 2.9647ˣ - 25 ≈ 0.0775
    f'(2.9647) = 2.9647ˣ (ln(2.9647) + 1) ≈ 52.33
    x₂ = 2.9647 - (0.0775 / 52.33) ≈ 2.96322 (practically solved already, but I continued until it converged for 6 decimal places, tedious but simple)
    3. f(2.96322) = 2.96322ˣ - 25 ≈ 0.00013
    f'(2.96322) = 2.96322ˣ (ln(2.96322) + 1) ≈ 52.16
    x₃ = 2.96322 - (0.00013 / 52.16) ≈ 2.9632198
    4. f(2.9632198) = 2.9632198ˣ - 25 ≈ 0
    x₄ ≈ 2.9632198

  • @BG-bq1qp
    @BG-bq1qp 18 วันที่ผ่านมา +1

    2.9632
    just do 2.5^2.5 and go up until you are above 25, then give it more decimals until you’re close enough

  • @YogeshPatil-tf7ic
    @YogeshPatil-tf7ic 21 วันที่ผ่านมา +2

    See, the question was: x^x = 25. Then, can't we write ( 25 ) as :- 5^2. Then x=5 and upper x=2. Can we do this??

    • @ikissbass6969
      @ikissbass6969 20 วันที่ผ่านมา

      We can't since only a single value of x has to be on both sides

    • @MC_GAMING-
      @MC_GAMING- 9 วันที่ผ่านมา

      X has to be same number because there only one variable

  • @odysseus9941
    @odysseus9941 16 วันที่ผ่านมา +1

    Die Gleichung x^x=25 kann nicht mit einfachen algebraischen Methoden gelöst werden, da x sowohl als Basis als auch als Exponent auftritt. Stattdessen wird sie mithilfe von numerischen Methoden oder der Lambert-W-Funktion gelöst.

  • @cyruschang1904
    @cyruschang1904 หลายเดือนก่อน +7

    x^x = 25 = 5^2
    xlnx = 2ln5
    let y = lnx, e^y = x
    ye^y = 2ln5
    y = lnx = W(2ln5)
    x = e^(W(2ln5))

  • @pizzaofdarkness4041
    @pizzaofdarkness4041 25 วันที่ผ่านมา +1

    I definitely need to use this equation while shopping at the grocery.

  • @mathguy37
    @mathguy37 16 วันที่ผ่านมา

    There's a different interesting way i found that appears to approximate a value without using the lambert W function
    so take the log of 25, the base matters to keep the number real, so just make a reasonable guess.
    Then just take the log of 25 with that as the base. Keep recursively doing that and the answer will approach the solution
    It takes a lot of logs to converge though, so it's easier to use recursive functions if inputting this into a calculator. (or using ans)
    100 logarithms gives ~2.96321977726 with a starting base of 3, which is very close to the true answer.
    Any starting base within a reasonable range gives a nearly equivalent answer as the number of logarithms increase. Using 5 gives 2.96321987478. I couldn't figure out range of bases that work though

  • @lool8421
    @lool8421 หลายเดือนก่อน +2

    just seeing the problem makes me think about using this function

  • @proking1033s
    @proking1033s 10 วันที่ผ่านมา

    Its simple
    2 power 2 is 4
    3 power 3 is 27
    Answer should be closer to 2.8 or 2.9
    Thats how objective questions work

  • @Guidussify
    @Guidussify หลายเดือนก่อน +15

    Ok, but where do I find the value of e^W(log(25))?

    • @HottyHelen
      @HottyHelen หลายเดือนก่อน

      @@Guidussify I wonder the same thing, as far as I can see this isn’t a function like sin or log, there’s no however long formula to find W of a value. I doubt it’s a button on any calculator you can buy. So you need to either use an analytical approximation, numerical methods like Newton Ralphson or software that probably use that. I just used Excel’s goal seek facility.

    • @cdmcfall
      @cdmcfall 28 วันที่ผ่านมา +4

      Iterative methods (brute force), mostly, or just run it through a Lambert W calculator. To evaluate this one, you would type in " e^(W_0(log(25))) " into the Wolfram Alpha search bar. Make sure you take a look at the graphs of y = x^x and y = 25. These sometimes have real solutions that aren't immediately obvious, as in the case of 2^x = x^2

    • @lanaforeal2588
      @lanaforeal2588 24 วันที่ผ่านมา +1

      To find the value of \( e^{W(\log(25))} \), we can utilize the property of the Lambert W function, which states that if \( y = W(x) \), then \( x = y e^y \).
      1. First, compute \( \log(25) \):
      \[
      \log(25) = \log(5^2) = 2 \log(5)
      \]
      2. Next, we find \( W(\log(25)) \). Since \( W(x) \) is the function that satisfies \( x = W(x)e^{W(x)} \), we need to express \( \log(25) \) in a suitable form for the Lambert W function.
      3. However, we can also use the property:
      \[
      e^{W(x)} = \frac{x}{W(x)}
      \]
      For our case, this means:
      \[
      e^{W(\log(25))} = \frac{\log(25)}{W(\log(25))}
      \]
      4. Since \( e^{W(x)} \) simplifies to \( x \) if \( x \) is of the form \( y e^y \), we conclude that:
      \[
      e^{W(\log(25))} = \log(25)
      \]
      Thus, the value of \( e^{W(\log(25))} = \log(25) \). If you need a numerical approximation, it can be calculated as follows:
      \[
      \log(25) \approx 3.2189
      \]
      So the final result is:
      \[
      e^{W(\log(25))} \approx 3.2189
      \]

  • @louiscarl7629
    @louiscarl7629 26 วันที่ผ่านมา +1

    Just put this in a solver that uses bisection, run some iterations and done, easy. Solves this whole class of thumbnail problems.

  • @GwnTim1
    @GwnTim1 หลายเดือนก่อน +5

    But if you’re gonna use an external source like Wolfram anyways I’d just plot it in Desmos and intersect it

    • @maddenbanh8033
      @maddenbanh8033 หลายเดือนก่อน +2

      Now find every complex solution.

    • @CMANIZABALLER
      @CMANIZABALLER 24 วันที่ผ่านมา

      @@maddenbanh8033none

  • @thorliebhammer7238
    @thorliebhammer7238 หลายเดือนก่อน +16

    Those who use "log" as the base e logarithm, are following the contemporary trend and are in the cool club.

    • @robertwarren4734
      @robertwarren4734 หลายเดือนก่อน +2

      If you mean 'contemporary' as 1906. That construction is found on Boltzmann's tombstone.

    • @partial-m4n
      @partial-m4n หลายเดือนก่อน

      In my country, it’s common to use log and we also learn like that
      So, ye, I can agree with that

  • @Dr_piFrog
    @Dr_piFrog 6 วันที่ผ่านมา +1

    Another mathematical solution video using (what I call the Willy Wanka function because of the plethora of TH-cam trick videos requiring its application) the Lambert W-function.

  • @bakersbread104
    @bakersbread104 17 วันที่ผ่านมา

    I think you should explain the Lambert equation for this to be educational at all

  • @syamprasad4455
    @syamprasad4455 6 วันที่ผ่านมา

    You can use newton raphson method to avoid look up table.

  • @harikeshavraman5506
    @harikeshavraman5506 22 วันที่ผ่านมา +6

    Obviously in modern world, we don't need this method to solve equations in daily basis
    - Excel Goal seek is going to help you out solve this one
    - Or if it's necessary to do it by a normal calculator,
    We know that the number and the power variable should be the same...
    1^1=1, 2^2=4, 3^3=27.....so x is somewhere near to 3 in order to get x^x=25... Do some trial & error,
    Try with x= 2.9 & 2.95,gives value as 21.9 & 24.3...so raise x to 2.96, gets 24.84 which is closer... Try 2.965,gets 25.1....try 2.963,gets 24.98....final try with 4 decimals....2.9633,gets 25......Believe me guys this just took me 2mins to do! I work on these equations on a daily basis in my work and I always prefer doing trial & error methods.... For complex eqns, we can use some numerical int methods like Simpson rule, etc to calculate x sooner

    • @mohitp66448
      @mohitp66448 18 วันที่ผ่านมา

      Literally did the exact same thing....

  • @viveksmenon123
    @viveksmenon123 19 วันที่ผ่านมา

    i have no idea about lamberts function. If I just want to approximate, I can just do a binary search between 2 and 3. 2.5^2.5, 2.75^2.75, 2.825^2.825, 2.93^2.93, 2.96^2.96

  • @wren51615
    @wren51615 26 วันที่ผ่านมา +1

    I saw the thumbnail and knew it was a little under three, and thought “oh god is it eulers number again”. Glad it wasn’t

  • @livewithals
    @livewithals 20 วันที่ผ่านมา

    Bit smaller than 3, that's what came first to my mind while looking at the equation.

  • @just-dl
    @just-dl หลายเดือนก่อน +17

    2.963 gets really close.

    • @itsmetanay
      @itsmetanay หลายเดือนก่อน +3

      2.9633 is approximately exact

    • @netanelkomm5636
      @netanelkomm5636 หลายเดือนก่อน +19

      @@itsmetanay"Approximately exact" is a funny combination of words.

    • @labyrinth2646
      @labyrinth2646 29 วันที่ผ่านมา

      ⁠@@itsmetanay2.96322 is closer

    • @MUI_Noam12
      @MUI_Noam12 28 วันที่ผ่านมา +1

      google says 2.963219774894 is close enough its a rounding error

    • @just-dl
      @just-dl 28 วันที่ผ่านมา

      @ Professor Google was always over the top! 🤣

  • @b213videoz
    @b213videoz 28 วันที่ผ่านมา +1

    Why do you keep calling log() with base 10 "a natural log" ?

  • @ilyashick3178
    @ilyashick3178 22 วันที่ผ่านมา

    Solution is only in case by using natural logarithm. Log is not natural

  • @Rone-q8v
    @Rone-q8v 27 วันที่ผ่านมา +1

    Why are there so many logs? Are we building a house?

  • @RunItsTheCat
    @RunItsTheCat 22 วันที่ผ่านมา +1

    Man Harvard really loves their Lambert W

    • @sanchellewellyn3478
      @sanchellewellyn3478 18 วันที่ผ่านมา

      I know, right? But it's really useful. I just wish it were easier to calculate its values.

  • @odysseus9941
    @odysseus9941 16 วันที่ผ่านมา

    Die Harvard University hat keine spezifische Aufnahmeprüfung wie z. B. eine standardisierte Prüfung, die alle Bewerber bestehen müssen. Stattdessen basiert das Aufnahmeverfahren auf einer ganzheitlichen Bewertung der Bewerbungsunterlagen, wobei viele Faktoren berücksichtigt werden.

    • @odysseus9941
      @odysseus9941 16 วันที่ผ่านมา

      Die Harvard University hat keine spezifische Aufnahmeprüfung wie z. B. eine standardisierte Prüfung, die alle Bewerber bestehen müssen. Stattdessen basiert das Aufnahmeverfahren auf einer ganzheitlichen Bewertung der Bewerbungsunterlagen, wobei viele Faktoren berücksichtigt werden.

  • @highlyeducatedtrucker
    @highlyeducatedtrucker 27 วันที่ผ่านมา +1

    Love the AI voice. "The Lambert double...(long pause)...u function..."

  • @PinoyRobots
    @PinoyRobots หลายเดือนก่อน +7

    how could I live without W Lambert Function ?

  • @netravelplus
    @netravelplus หลายเดือนก่อน +1

    Amazing problem, scaring in the beginning but as you started explaining, the fog cleared and the brain sparkled.

  • @yuki7951
    @yuki7951 หลายเดือนก่อน +1

    I expected Lambert function to show up. I'm already used to seeing those videos XD

  • @laplacia
    @laplacia 27 วันที่ผ่านมา

    (x^x)' = x(x^(x-1)) = x^x which makes its taylor expansion very simple.

  • @DailyWorkoutEnjoyer
    @DailyWorkoutEnjoyer 21 วันที่ผ่านมา +5

    "And why do we need to know the answer to this?"
    ".. For...... uh... Science!"

  • @DexlabHurts
    @DexlabHurts 9 วันที่ผ่านมา

    Isn't Lambert W function only valid when w is a complex number?!

  • @maroly8342
    @maroly8342 16 วันที่ผ่านมา

    The solution is between 2 and 3. No need to be more precise on that 😅

  • @Rise6474
    @Rise6474 19 วันที่ผ่านมา +16

    Everyone in the comments are WRONG. The ACTUAL answer is: X = 2.96321977489346

    • @chrupek439
      @chrupek439 17 วันที่ผ่านมา +3

      2.963219774893456328309^2.963219774893456328309 = 25.000000000000000000159053596577 so nope, still working on it
      i got to:
      2.9632197748934563283059504789757^2.9632197748934563283059504789757 = 25.000000000000000000000000000001
      my calc wont let me add more numbers 😂

    • @kateknowles8055
      @kateknowles8055 15 วันที่ผ่านมา +1

      .....approximately..................................

    • @oAnshul
      @oAnshul 15 วันที่ผ่านมา +1

      ​@@chrupek439there's a decimal after 2 not a comma

    • @chrupek439
      @chrupek439 14 วันที่ผ่านมา

      @@oAnshul in polish schools we are taught to use comma, for larger numbers we just leave space between every last three digits. But I changed it for you anyway :)

  • @randerson4009
    @randerson4009 28 วันที่ผ่านมา

    Why not just use an iterative approximation method on the original equation to the precision desired? This avoids the rearranging of the equation and finding the value of the resulting Lambert W.

  • @studentofspacetime
    @studentofspacetime 12 วันที่ผ่านมา

    So basically, you didn’t solve the problem. You just gave it a name.

  • @Rudrakunjir
    @Rudrakunjir 14 วันที่ผ่านมา

    Shouldn’t you be using ln for natural log. Log is for base 10. Atleast I think. Cus I got confused at the lambert w part.

  • @Mr.Icecream
    @Mr.Icecream 18 วันที่ผ่านมา

    THIS IS 8TH GRADE EXPONENTS CHAPTER QUESTIONS IN INDIA , and theirs no harvard entrance exams

  • @sohayb1m-582
    @sohayb1m-582 หลายเดือนก่อน +1

    I actually found x 2.964 so im very proud of my self

  • @Vega1447
    @Vega1447 หลายเดือนก่อน +3

    Just solve x * log(x)= log 25. Using Newtons method x=x-(x*log(x)-l25)/(1+log(x)) starting with x=3 you get 10 digit accuracy after 2 or 3 iters. x=2.963219774893456.

  • @Antonio-v2j
    @Antonio-v2j 2 หลายเดือนก่อน +21

    Me who thought it was 5^2 = 25 🥲

    • @brain_station_videos
      @brain_station_videos  2 หลายเดือนก่อน +7

      thats why i mentioned it in the video 🤣

    • @just-dl
      @just-dl หลายเดือนก่อน

      That was my first thought then I attacked my calculator for the best approach: trial and error with guessing. 😎

  • @hereticalgames3695
    @hereticalgames3695 15 วันที่ผ่านมา

    Why people feel the need to solve using algebra over trial and error I’ll never understand.

    • @hereticalgames3695
      @hereticalgames3695 15 วันที่ผ่านมา

      Edit: 5^2 =25 so the range must be 2-5 3^3=27 so the range is 2-3 punch in like 2.9 and you’ll find it short 2.96-2.97 is the next range how many decimals do you practically need. It turns into simple busy work fast.

  • @bowiebrewster6266
    @bowiebrewster6266 20 วันที่ผ่านมา

    Lambert w function is cheating. Might aswell say i have the bowie-w function is the solution to a = x^x. So we get bowie(25)

  • @Slash1066
    @Slash1066 หลายเดือนก่อน +2

    If its not 5 I'm all out of ideas

  • @luclacourse424
    @luclacourse424 24 วันที่ผ่านมา

    the only thing that doesnt make sense to me in this equation is the use of x for 2 var...in programmation language x = 5 exponential x = var

  • @Pr.bln.arab44
    @Pr.bln.arab44 15 วันที่ผ่านมา

    For me , i never imagine a brut numer like 1 , i see wave and 1 in the top

  • @johnjr2jr2
    @johnjr2jr2 หลายเดือนก่อน +1

    Nice. It makes a lot for the planet

  • @JonJenkins1982
    @JonJenkins1982 หลายเดือนก่อน

    I figured it out in less time using a calculator and guessing and got more precision than the algebraic way

    • @maddenbanh8033
      @maddenbanh8033 หลายเดือนก่อน

      He used an arbitrary amount of precision.

  • @carloalbertocolaiacovo4182
    @carloalbertocolaiacovo4182 หลายเดือนก่อน +1

    Bro you forget the modul inside the natural log when you do ln x^x =
    x ln |x|
    So you resolve that for x>o and for x

  • @Boyscrazy719
    @Boyscrazy719 20 วันที่ผ่านมา +1

    Harvard entrance exam 🤡 JEE Advanced ☠️☠️

  • @АлександрБедин-х2ш
    @АлександрБедин-х2ш 26 วันที่ผ่านมา

    What is the hardness of the task? If it is known in advance in which functions it is allowed to give an answer, then it is solved in 3 lines for any 9th graders.

  • @AndrewUnruh
    @AndrewUnruh 19 วันที่ผ่านมา

    OK...I guess my problem with the solution is this...There is no closed form solution of the Lambert W function so we have to use numerical methods. But if that is the case, I can just use a numerical method to solve for the original equation without the use of the Lambert W function, right? I guess the advantage is that if you don't know how to write a numerical solution, you can use an on-line Lambert W function calculator.

  • @saminyead1233
    @saminyead1233 25 วันที่ผ่านมา

    Or, you can solve this numerically, since you know the answer is between 2 and 3.

  • @donsimon2830
    @donsimon2830 หลายเดือนก่อน +1

    Have you heard the one about the mathematician and his logs. Well, he worked them out using a pencil.

  • @pingkai
    @pingkai 29 วันที่ผ่านมา

    This is essentially saying we define the solution x^x = y and F(y), wtf.

  • @SuccessRedefined_1
    @SuccessRedefined_1 23 วันที่ผ่านมา

    Now you have a new problem :
    What is the value of W(ln(25)) ?
    For which you will need a calculator 😂

  • @chair1694
    @chair1694 หลายเดือนก่อน +2

    So good....as always

  • @eclxpse2
    @eclxpse2 หลายเดือนก่อน +2

    Bruh just guess and check, i got x = 2.9634

  • @SuryaKant-u4h
    @SuryaKant-u4h ชั่วโมงที่ผ่านมา

    x^x can be written as x X x and 25 can be written as 5 X 5 So x is 5

  • @vatsalmakol7
    @vatsalmakol7 19 วันที่ผ่านมา +1

    2.9634 approx

  • @RyanLewis-Johnson-wq6xs
    @RyanLewis-Johnson-wq6xs หลายเดือนก่อน +7

    2^2=4 3^3=27 4^4=256 5^5=3125

    • @Why553-k5b_1
      @Why553-k5b_1 หลายเดือนก่อน +3

      and? what is purpose of this comment?

  • @qwerty1423a
    @qwerty1423a 2 หลายเดือนก่อน +16

    yea, just the click baiting shit as always

  • @Esterified80
    @Esterified80 หลายเดือนก่อน +1

    Absolute headache

  • @7F0X7
    @7F0X7 18 วันที่ผ่านมา

    Thanks for the video. But I took calc 1 in highschool and the "W" function was never taught. I highly doubt such a niche constant function would be part of any entrance exam except maybe those chinese entrance exams they give to poor, rural students for the express purposes of lowering their pass rates so the rich urban kids can dominate (this actually happens, look it up). You were too fast & loose as you alternated between saying "log" and "natural log" yet only writing "log". The entire problem should have been "natural log" only and written as "ln".

  • @ronaldbryant5215
    @ronaldbryant5215 20 วันที่ผ่านมา

    Calculators are not allowed - said all of my college math teachers.

  • @mikerood7193
    @mikerood7193 18 วันที่ผ่านมา

    I got 2.96322 in my head after a few minutes

  • @shampudey9952
    @shampudey9952 27 วันที่ผ่านมา +1

    2.963^2.963422111 is more accurate its about 24.9999999

  • @aoichan4353
    @aoichan4353 22 วันที่ผ่านมา

    i thought the answer for x to the power of x will have 0.50 as the value of x

  • @0943kt
    @0943kt หลายเดือนก่อน +1

    2:16 im pretty sure x is not equal to e^log(x). if we apply ln, that gives us ln(x)=log(x), which the only solution to this is x=1. you need to use ln instead of log at the start so e and ln cancels

    • @adw1z
      @adw1z หลายเดือนก่อน +2

      No because log means log base e

    • @0943kt
      @0943kt หลายเดือนก่อน

      @ that becomes ln

    • @adw1z
      @adw1z หลายเดือนก่อน +1

      @@0943kt "log" means "log base e" in more conventional mathematics

    • @0943kt
      @0943kt หลายเดือนก่อน

      @@adw1z i thot by default log means log base 10?

    • @adw1z
      @adw1z หลายเดือนก่อน +1

      @@0943kt well it depends on context and what the usage of it is. Majority of the time in published papers, log will mean natural log. I found it’s mainly in school that they distinguish between ln and log. The reason is log base e is used pretty much everywhere all the time, whereas logs in other bases are very rarely used.
      It can be confusing, for example one of my courses used log, which actually meant log base 2 implicitly. So just be wary of the context of the problem; here it’s pretty obvious log meant base e, and he specified by saying “natural log”

  • @BiagioLatufara
    @BiagioLatufara หลายเดือนก่อน

    Shouldn’t it be e^ln(x), instead of e^log(x)

  • @justdeko5522
    @justdeko5522 22 วันที่ผ่านมา

    I guess it is called lambert W function for a reason 💀

  • @dougpage1271
    @dougpage1271 21 วันที่ผ่านมา

    I will be a truck driver.

  • @sheltondany8209
    @sheltondany8209 15 วันที่ผ่านมา

    sitting and finding this thru trial and error also works.. if you do jack about W()

  • @kateknowles8055
    @kateknowles8055 15 วันที่ผ่านมา

    x = approx 2.96322

  • @psydhant
    @psydhant 18 วันที่ผ่านมา +1

    How is log(x) equal to ln(x)?

  • @toppo722
    @toppo722 หลายเดือนก่อน +6

    me be like -
    1^1 = 1
    2^2 = 4
    3^3 = 27
    so it would be approx ~2.9 something

  • @jose_k_martin
    @jose_k_martin หลายเดือนก่อน +1

    I find that answer before the video ends,because i am an indian

  • @Realalexandro
    @Realalexandro หลายเดือนก่อน +1

    f(x)=x^x IS NOT a purely INCREASING function because on the half-interval of (0;1/e] it effectively decreases. You can calculate its derivative to confirm that.
    Next given that lim f(x->0) = 1 (which can be proved using L'Hospital's rule, also known as Bernoulli's rule that allows evaluating limits of indeterminate forms using derivatives), you should
    at least say that the potential max(f(x)) on (0;1/e] is 1, although it can't be achieved because 0^0 is an undefined expression! So on the decreasing "end" f(x) < 25 and can not have any solutions.
    On (1/e; +infinity) though f(x) is monotonously increasing, so on this place of the plot there can be no more than one solution that you've actually found.
    IMHO Harvard guys are pretty dumb to ask such questions, cause transcendent equations of such nature in general form CAN BE SOLVED ONLY USING W-Lambert function (which can't be represented in elementary functions) and moreover if you know this W-Lambert technique once and for all times all of these tasks are usually pretty easy to solve in terms of W-Lmb function.
    So producing correct solution only demonstrates that you know what W-Lambert is and how to apply it directly, nothing more! No guess, no creativity or originality of thought process here needed.

  • @pw6564
    @pw6564 หลายเดือนก่อน +1

    On peut utiliser Excel et la fonction : "valeur cible"

  • @ant0n1dze
    @ant0n1dze หลายเดือนก่อน

    Дружище, ты не написал, как бы ты вычислил функцию Ламберта без всяких там wolfram и т.д. Это явно не примут на экзамене

  • @FallenImmortal69
    @FallenImmortal69 20 วันที่ผ่านมา

    Ok so..... i haven't learnt it yet but in advance what is log?

    • @FallenImmortal69
      @FallenImmortal69 20 วันที่ผ่านมา

      Forget it I gave up understanding it I will learn it in 11th or 12th then I will come back to this vid