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

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**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:

www.janestreet.com/what-we-do/

Ask them for a job here:

www.janestreet.com/join-jane-street/

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.

www.think-maths.co.uk/log-meme

CORRECTIONS

- 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:

www.patreon.com/standupmaths

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/ **Entertainment**

Wolfram StahlMonth 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".

Frank Anthony Overton Jr.29 days agoBlox117 just the top half of it.

Blox117Month ago@EnNarr91 what??

EnNarr91Month ago@Blox117 What?

Gibran AMonth ago^{+1}A Parker Division

astronelsonMonth ago^{+1}Matt previously worked for Enron.

England is my cityDay ago1:50 if you multiply the factors of 28 you get 28^2

Badhbhchadh3 days ago6:46 Yep, 0! = 1.

TheRealDavis6603 days agoWell, 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.

ViliamF7 days agowhat's the name of the song in outros?

Laurelindo5 days agoI'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.

Nobodyimportant8 days agoThis guy is a G, smart and social

Laurelindo10 days agoMatt in the thumbnail: "WOW that looks amazing! And you won't believe what happens in this video!".

Baskar M14 days agoName of the youtube channel is standupmath.....

But he is always sit.....🤔

Kieran Sinclair-Lomax14 days agoThe 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

lukey666lukey20 days agoI have learnt that Log Trolls are a thing, everyday is a school day

amigalemming20 days ago9:30 But Jane Street is specialized on functional programming (OCaml), not Python (as far as I know).

William Taylor20 days agoI 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]20 days agoCongrats, you made a very outdated meme

Altoclarinets20 days agoThis week on standupmaths: Does Matt Parker Actually Know Arithmetic?

Allan Boone20 days agolog(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 Scheper21 day agoGreat vid, but please don't ever, ever use that horn sound again.

Seth Don21 day agoMatt, look out for flammable maths! He is a nuclear bomb in the math community. Beware!

mrkv4k22 days agoYou can use multiple ones. Like 1 + 1 + 2 + 4 = 2*4

Wafik Lotfallah22 days agoxy = x + y implies y = x/(x - 1).

Thus, x and y are positive integers iff x = y = 2.

Mart R22 days agoThe 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 wrandom23 days agoHere is a proof if one tolerates only one 1.

Parker Lee23 days agoHey, 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-boiled23 days ago6:48 0 is not equal to ZERO!, which is equal to 1

BobC23 days agoSo, 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 Marra24 days agoThe faces in the thumbnail and in the first 3 seconds are priceless.

Meaning I wouldn't really pay to see them.

RUSapache24 days ago3 x 1.5 = 3 + 1.5

log(3+1.5)=log(3)+log(1.5)

Narayan Bhat24 days agoi can sense the black curtain over there

Logan True24 days agoEverytime I hear Log Troll, I think of D&D trolls armed with tree logs as bludgeons.

Robert Telarket25 days agoWho are you? Are you at a university from Britain or down under? Your name please.

Taiken6425 days agoIs there a way to rationalize "add ones until the sum equals the product of the original two numbers" without being explicit about it?

hexa26 days agoThumbs down for making this 10 minutes.

hexa26 days agoAll you had to say is that log(1)=0

Zyxok Unum26 days ago1+2+3=1*2*3

Alex King26 days ago^{+1}Can you do another Rubik’s cube video?

Alex King26 days ago^{+1}For the one person who sees this I just want to tell you

That God loves you ❤️❤️❤️❤️❤️

Just My Opinion26 days agoWhat is this suppose to be? Advertisement?

movax20h26 days agoWould prefect number works with a minor tweaks of putting some rational factor in front of the one log?

Willem van de Beek26 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 Spalding26 days ago@3:36 thought of that before it came up

Nexus Clarum26 days agoso is 6 maximum-over-perfect? (｡◕‿◕｡)

qrpnxz26 days agoEven though this shouldn't work by all known laws of aviation, the log still flies.

Harrison Haines27 days agoDoesn'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)

and

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!

Harry Rispin25 days agoYOu can't log a negatve number

Everett Kelly27 days agoThere 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 Scanlon27 days agoHalf Life 3 confirmed...

sur-taka27 days agolog(1+3+1+3+1)=log(1)+log(3)+log(1)+log(3)+log(1)

Derek Donner27 days ago1 + 2 + 3 = 6 = 2 * 3

Felix Stenger27 days agowhats the sub reddit he used the screenshot from?

Dave lowinger27 days agoN÷1.618...=N•0.618...

thomas guitard27 days ago^{+2}log(1+2+3+...)=log(-1/12)

Imie Nazwisko27 days agoWhat about branches or sticks?

Believer of LIght27 days agomath noobs fascinate me ... how gullible

j. rodman27 days agoCapital pi means the product of the set? Math notation sucks.

Benjamin Newlon27 days agoMatt is bald!?

John Godot27 days agoSomeone 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. Bane27 days agoI was hoping you'd do the log of Lucas numbers

Spencer D28 days agoFor 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

Valdemar28 days agoOi Matt! What ever happened to the three sided coin? Any exiting news? I need to know!

jeuxinfini28 days agolog(1 + 2 + 3) = log(6) = log(2*3) = log(2)+log(3) = log(1)+log(2)+log(3)

Bitcoin Israel28 days agoJust 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.

thexvid.com/video/xCtRPtjGGXI/video.html

Robert McGarry28 days ago0! = (1/2) 2!

Yami28 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 monedulas28 days agoRemember when this dude has hair?

Eva Moniz28 days agolog(1+2+3+4+5+6+7+8+9+10) = log(10)+log(11)-log(2)

Dhruve Mital28 days agothe one channel where i didnt expect air-horns, thats even bigger than a log troll

Михаил Сибирев28 days agoCan you build a square of S=3 ?

Morgan Lasky28 days ago3:07 did you mean that 101 looks like lol ?

Peter Pike28 days agoHalf of two is tv.

whoijacket28 days ago^{+4}Matt. Buddy. You’re allowed to do multiple takes. You don’t have to keep in the brain farts.

Howard You Doing29 days agoI’m confused of what the graph represents

Oisin Smith29 days ago^{+17}1950s: I bet in the future we will have flying cars

2019: half of two is two

sdk24 days ago*Its b e t t e r*

kundogb29 days agoHahahahah