What's the story with log(1 + 2 + 3)?

  • Published on Jun 14, 2019
  • This is my deep dive into the log(1 + 2 + 3) = log(1) + log(2) + log(3) log troll meme. I'm not going to link to any of the online discussions incase I accidentally encourage brigading. If you want to join in constructively, you can google them.
    Huge thanks to Jane Street for becoming my channel's principle sponsor. If you're curious, this is what they do:
    Ask them for a job here:
    We make Think Maths teaching resources to go with Stand-up Maths videos. For this one we have a worksheet of questions you can give your students before they watch the video. Plus I provide my excel file for the plot of the max values.
    - I mis-spoke and said "two" instead of "four" and "one" instead of "zero" but tried to fix both with titles in the edit. Sorry I did not have time to re-film it!
    - Yes, my camera autofocus is annoying. I swear it has broken somehow; I thought I'd set it up right this time. I think Jane Street might have to get me a new camera.
    - Let me know if you spot anything else!

    Thanks to my Patreon supporters who help make these videos possible. Here is a random subset:
    Michael Lehenbauer
    Richard Dickins
    Barry Salter
    Maksym Borodin
    James Williams
    Sarah Gerweck
    Support my channel and I can make more maths videos:
    Music by Howard Carter
    Filming and editing by Matt Parker
    Design by Simon Wright
    MATT PARKER: Stand-up Mathematician
    Website: standupmaths.com/
    Maths book: wwwh.umble-pi.com
    Nerdy maths toys: mathsgear.co.uk/
  • EntertainmentEntertainment

Comments • 706

  • Wolfram Stahl
    Wolfram Stahl Month ago +1771

    Jane Street sponsor Matt Parker because "they just like maths and they use maths to solve complex problems in the financial world."
    Matt: "half of two is two".

  • England is my city

    1:50 if you multiply the factors of 28 you get 28^2

  • Badhbhchadh
    Badhbhchadh 3 days ago

    6:46 Yep, 0! = 1.

  • TheRealDavis660
    TheRealDavis660 3 days ago

    Well, log(4+3+1+1+1+1+1)
    You can do loads of whole number solutions if you don't mind filling it with 1s
    Edit: Never mind, you addressed this in the video.

  • ViliamF
    ViliamF 7 days ago

    what's the name of the song in outros?

    • Laurelindo
      Laurelindo 5 days ago

      I'm not sure if it has a real name, but you can listen to it all you want if you search for the video "STANDUPMATHS FULL THEME SONG - Howard Carter
      " here on TheXvid.

  • Nobodyimportant
    Nobodyimportant 8 days ago

    This guy is a G, smart and social

  • Laurelindo
    Laurelindo 10 days ago

    Matt in the thumbnail: "WOW that looks amazing! And you won't believe what happens in this video!".

  • Baskar M
    Baskar M 14 days ago

    Name of the youtube channel is standupmath.....
    But he is always sit.....🤔

  • Kieran Sinclair-Lomax
    Kieran Sinclair-Lomax 14 days ago

    The formula I made for any two numbers is n*(n+1/n)=n+(n+1/n). It’s a generalised equation that includes 2+2=2*2 and 101+1.01=101*1.01. Like or reply to this comment if you think this formula is better than Matt’s explanation :p

  • lukey666lukey
    lukey666lukey 20 days ago

    I have learnt that Log Trolls are a thing, everyday is a school day

  • amigalemming
    amigalemming 20 days ago

    9:30 But Jane Street is specialized on functional programming (OCaml), not Python (as far as I know).

  • William Taylor
    William Taylor 20 days ago

    I always check 3 4 5, its got to be 4 5 6 7, the problem is you need an equality because it creates a unit system of equality, 5 billion, basic constants.

  • Dinamy [Kw4]
    Dinamy [Kw4] 20 days ago

    Congrats, you made a very outdated meme

  • Altoclarinets
    Altoclarinets 20 days ago

    This week on standupmaths: Does Matt Parker Actually Know Arithmetic?

  • Allan Boone
    Allan Boone 20 days ago

    log(a+b+c)=log(a)+log(b)+log(c) if and only if a+b+c=a*b*c and a,b,c>0.

  • Mik Scheper
    Mik Scheper 21 day ago

    Great vid, but please don't ever, ever use that horn sound again.

  • Seth Don
    Seth Don 21 day ago

    Matt, look out for flammable maths! He is a nuclear bomb in the math community. Beware!

  • mrkv4k
    mrkv4k 22 days ago

    You can use multiple ones. Like 1 + 1 + 2 + 4 = 2*4

  • Wafik Lotfallah
    Wafik Lotfallah 22 days ago

    xy = x + y implies y = x/(x - 1).
    Thus, x and y are positive integers iff x = y = 2.

  • Mart R
    Mart R 22 days ago

    The first thing I thought when seeing this "log troll" thing (in this video, I might add) was similar the "hang on bit" - given log(1)=0, any number should be able to be used. Maybe not as impressive if there's repetition, but still possible.

  • hey wrandom
    hey wrandom 23 days ago

    Here is a proof if one tolerates only one 1.

  • Parker Lee
    Parker Lee 23 days ago

    Hey, Matt, theres a problem I've been struggling with and I wondered if you had any insight. I've been trying to find a function f(x) such that the derivative of f at a (for all a in the domain of f) Is equal to the area under the curve f(x) from 0 to a. I feel as though there is more than one solution. If you could help me tackle this, it would be much appreciated.

  • Soft-boiled
    Soft-boiled 23 days ago

    6:48 0 is not equal to ZERO!, which is equal to 1

  • BobC
    BobC 23 days ago

    So, it seems there is no limit Matt will ever reach where he will deem a re-shoot necessary... Bring on the amusing text overlays!

  • Diego Marra
    Diego Marra 24 days ago

    The faces in the thumbnail and in the first 3 seconds are priceless.

    Meaning I wouldn't really pay to see them.

  • RUSapache
    RUSapache 24 days ago

    3 x 1.5 = 3 + 1.5

  • Narayan Bhat
    Narayan Bhat 24 days ago

    i can sense the black curtain over there

  • Logan True
    Logan True 24 days ago

    Everytime I hear Log Troll, I think of D&D trolls armed with tree logs as bludgeons.

  • Robert Telarket
    Robert Telarket 25 days ago

    Who are you? Are you at a university from Britain or down under? Your name please.

  • Taiken64
    Taiken64 25 days ago

    Is there a way to rationalize "add ones until the sum equals the product of the original two numbers" without being explicit about it?

  • hexa
    hexa 26 days ago

    Thumbs down for making this 10 minutes.

  • hexa
    hexa 26 days ago

    All you had to say is that log(1)=0

  • Zyxok Unum
    Zyxok Unum 26 days ago


  • Alex King
    Alex King 26 days ago +1

    Can you do another Rubik’s cube video?

  • Alex King
    Alex King 26 days ago +1

    For the one person who sees this I just want to tell you

    That God loves you ❤️❤️❤️❤️❤️

  • movax20h
    movax20h 26 days ago

    Would prefect number works with a minor tweaks of putting some rational factor in front of the one log?

  • Willem van de Beek
    Willem van de Beek 26 days ago +1

    Oof, lots of trolls in the comments.
    Thank you for showing that capital pi is the mass product. I knew capital sigma was the mass sum, but I was completely unaware of the mass product.
    I learned something new from your video, so thank you for this! :)

  • Cameron Spalding
    Cameron Spalding 26 days ago

    @3:36 thought of that before it came up

  • Nexus Clarum
    Nexus Clarum 26 days ago

    so is 6 maximum-over-perfect? (。◕‿◕。)

  • qrpnxz
    qrpnxz 26 days ago

    Even though this shouldn't work by all known laws of aviation, the log still flies.

  • Harrison Haines
    Harrison Haines 27 days ago

    Doesn't -1 -2 and -3 work for this as well.
    Log ( -1 + -2 + -3) = log (-6)

    where m = ℤ
    Log (-1) = (2m + 1)*i*pi
    Log (-2) = (2m + 1)*i*pi + log(2)
    Log (-3) = (2m + 1)*i*pi + log (3)
    Log (-6) = (2m + 1)*i*pi + log(6)
    we know log (2) + log(3) = log(6), and for an infinite set of ms (2m+1)*i*pi*3 = (2m + 1)*i*pi
    and so for an infinite set of m's log (-1 + -2 + -3) = log (-6).
    A log troll and an i troll all in one!

  • Everett Kelly
    Everett Kelly 27 days ago

    There is a pattern to these sum- product sets! Add a "1" to the set and add 1 to to last number.
    2 , 2
    1 , 2 , 3
    1 , 1 , 2 , 4
    1 , 1 , 1 , 2 , 5

  • Brian Scanlon
    Brian Scanlon 27 days ago

    Half Life 3 confirmed...

  • sur-taka
    sur-taka 27 days ago


  • Derek Donner
    Derek Donner 27 days ago

    1 + 2 + 3 = 6 = 2 * 3

  • Felix Stenger
    Felix Stenger 27 days ago

    whats the sub reddit he used the screenshot from?

  • Dave lowinger
    Dave lowinger 27 days ago


  • thomas guitard
    thomas guitard 27 days ago +2


  • Imie Nazwisko
    Imie Nazwisko 27 days ago

    What about branches or sticks?

  • Believer of LIght
    Believer of LIght 27 days ago

    math noobs fascinate me ... how gullible

  • j. rodman
    j. rodman 27 days ago

    Capital pi means the product of the set? Math notation sucks.

  • Benjamin Newlon
    Benjamin Newlon 27 days ago

    Matt is bald!?

  • John Godot
    John Godot 27 days ago

    Someone noted that by the Vieta formulas, the roots of any polynomial of degree n such that a_{n-1} = a_0*(-1)^n have this property. Since those can be hard to obtain, the particular case for quadratics is that log(½[x+√x(x-4)] + ½[x-√x(x-4)]) = log(½[x+√x(x-4)]) + log(½[x-√x(x-4)]).
    So, you can just pick an x larger than 4, and you can find two numbers that satisfy the property with that formula. Then, you can further decompose each term of the logs, until they're no longer larger than 4.

  • Durin S. Bane
    Durin S. Bane 27 days ago

    I was hoping you'd do the log of Lucas numbers

  • Spencer D
    Spencer D 28 days ago

    For a two number log troll we have the equation x+y=xy. This means x+y-xy=0. So x-xy+y-1=-1. So (x-1)(1-y)=-1 or (x-1)(y-1)=1. The only integer factorizations of 1 are 1(1) and -1(-1). The first case gives x=y=2 and the second gives x=y=0, but we can’t take the log of 0. So log(2+2)=log(2)+log(2) is the only solution for 2 terms

  • Valdemar
    Valdemar 28 days ago

    Oi Matt! What ever happened to the three sided coin? Any exiting news? I need to know!

  • jeuxinfini
    jeuxinfini 28 days ago

    log(1 + 2 + 3) = log(6) = log(2*3) = log(2)+log(3) = log(1)+log(2)+log(3)

  • Bitcoin Israel
    Bitcoin Israel 28 days ago

    Just to help Matt a bit with his math - here's a video which explains that 2+2=4, from which we can deduce that half of 2 is most definitely *not* 2.

  • Robert McGarry
    Robert McGarry 28 days ago

    0! = (1/2) 2!

  • Yami
    Yami 28 days ago +2

    2/2 = 2
    The identity of addition is 1
    Says 1, correction says 0! which equals 1
    True Parker Square Logic

  • corvus monedulas
    corvus monedulas 28 days ago

    Remember when this dude has hair?

  • Eva Moniz
    Eva Moniz 28 days ago

    log(1+2+3+4+5+6+7+8+9+10) = log(10)+log(11)-log(2)

  • Dhruve Mital
    Dhruve Mital 28 days ago

    the one channel where i didnt expect air-horns, thats even bigger than a log troll

  • Михаил Сибирев

    Can you build a square of S=3 ?

  • Morgan Lasky
    Morgan Lasky 28 days ago

    3:07 did you mean that 101 looks like lol ?

  • Peter Pike
    Peter Pike 28 days ago

    Half of two is tv.

  • whoijacket
    whoijacket 28 days ago +4

    Matt. Buddy. You’re allowed to do multiple takes. You don’t have to keep in the brain farts.

  • Howard You Doing
    Howard You Doing 29 days ago

    I’m confused of what the graph represents

  • Oisin Smith
    Oisin Smith 29 days ago +17

    1950s: I bet in the future we will have flying cars
    2019: half of two is two

    • sdk
      sdk 24 days ago

      *Its b e t t e r*

  • kundogb
    kundogb 29 days ago