Logarithms, Explained - Steve Kelly

View full lesson: ed.ted.com/less...
What are logarithms and why are they useful? Get the basics on these critical mathematical functions -- and discover why smart use of logarithms can determine whether your eyes turn red at the swimming pool this summer.
Lesson by Steve Kelly, animation by TED-Ed.

[@goldenduck3931]

He sounds like the teacher that discusses enthusiastically but then gives a quiz right after the lesson. It made me nervous watching this.

[@hero9402]

yeaaaas felt the same way

[@michaelaramis1210]

the sound of betrayal

[@Frlja]

I had exactly that in mind :D

[@avery8852]

Same lmfao

[@mew1405]

FRRRR

[@crimsonfox9827]

An episode a day keeps the bad grades away

[@lpawowp]

So true

[@SreeragNairisawesome]

nevermind....got it

[@TheMrsundaygamer]

10^(-7.400116928) = 0.0000000398

[@entertainingyou5274]

ture

[@swatikumari9782]

True that!

[@simranmalhotra7364]

Thank you TED-Ed... My teachers at school never explained what log actually meant... they just started with its application in differentiation... Thank you So much!! I wish teachers would start explaining the same way!

[@chriswebster24]

This is nonsense, and it’s extremely dangerous. No decent eye doctor would ever recommend using logarithms after swimming. This video needs fo be removed, immediately, before it causes someone to go blind. I’m reporting it to the KZbin police. I hope the people who posted this BS have fun in prison. Say hi to Bubba for me, ya jerks. Don’t drop your soap.

[@stevekru6518]

That would require teachers to understand logs.

[@jimwinchester339]

Please see my separate comment above - about what logs actually mean.

[@spacegeek6166]

Same lol My teachers never explained But during my uni interview i was asked this ques…..

[@fos1451]

@@spacegeek6166how can ou don’t know what log is?

[@thegreenpianist7683]

Legend says he is still saying Zero

[@KevDoesEverything]

TheGreenPianist legends say his eyes never turned back to normal

[@leesf481]

This has reached over 100 likes Congrats

[@TheKellisunshyne]

It's not a legend...if you listen carefully on a quiet summer's eve you can still hear him sayin,"the base raised to what power equals the number?"

[@anvayaiyer5614]

llloooooooooooogarithms

[@oooooooooookkk333]

I am from 2024

[@KevDoesEverything]

Tbh I watched this because my teacher told me to skip a logarithm question on a practice sheet because we "don't know the material" so I'm tryna stay ahead of the game here

[@PokeMageTech]

Good on you!

[@ayushsharma4894]

so did you pass

[@DCBfanboy]

👌👌

[@enzoqueijao]

Nowadays, Kevin is an unstoppable machine of knowledge, motivated only by his desire of staying ahead of everyone. This is what mathematics do to you.

[@superlambmilkshake4904]

I swear I hate those kinds of mediocre teachers

[@divyjain5095]

Honestly this one feels like a necessity of every upcoming batch and they made it 10 years ago and now i can guess how many students were helped out of this thanks to steve and the TED ED team

[@lylefaraday4691]

..llLOOOGgarithm!

[@MrJasonJasonJason100]

+Lyle Faraday More like LOAG arithms.

[@random-mn5uc]

L-aaawww- g-rithm

[@tronglinhtieu8980]

Lyle Faraday 😙👽👀♥*)👃👣👣💀💙❤👃👾👂

[@suyogyarmj3756]

Dude had me literally ROFL with the llLLLoooogarithm

[@myagrimm4719]

Wow, I studied logarithms last semester. Yesterday in chemistry a logarithm came up in an equation and I was easily able to figure out what I had to do by using my calculator, but I realized, I don't know how logs really work. When I did them in class, I just remembered how to use them, not WHY. So I looked it up today, and this short video helped me so much! I feel like I have a better understanding than when I was actually doing logs in class. I was missing that fundamental information of why they actually work

[@Scam_Likely.]

It's amazing how much math (and things in general) become easier when you understand not just how it works but WHY it works. I wish that concept was more prevalent in schooling

[@lowurcase3238]

@@Scam_Likely. Agreed. I think the primary focus in school should shift to helping students understand the entirety of a concept.

[@craigpo2927]

Algorithm logArithm *What*

[@shen144]

WWWWWWWWWOOOOOOAAAAAAAAHHHHHHHHH

[@aryanjha6245]

Anagram

[@cjfdnqkn4374]

Rhythm

[@Tomiokasan-]

Somebody was like . Wait a min let me just .. and made these two words 😂

[@mohammed.a1980]

Man this has to be the best and simple explanation of Logarithms which can be easily understood by even a primary school kid and PhD student!!!😃

[@kimll88]

I wish I had Ted Ed when I was in school. Makes learning so much more fun.

[@scoutgaming737]

So basicaly a square root, but you're finding the power instead of the base

[@sparklenights5421]

lol yeah

[@salthesadmanshark5645]

This was the most wholesome ted ed video i'ven ever seen , and i have seen quite a lot of them.

[@YianniGaliatsatos]

The inflection of this man's voice makes this video all the more entertaining

[@longlivelemmy7733]

Sometimes i ask myself: Why do we go to School? I mean watching a two minutes Videos about a Topic is way more effective than sitting in class and listening ti the boring teacher....

[@btdpro752]

long live Lemmy maybe if you paid attention to your teacher you wouldn't think that

[@btdpro752]

long live Lemmy the teacher isn't boring the teacher has to teach 20 students. If you think you can do that everyday and make it interesting then be my guest. This also isn't for anyone .

[@btdpro752]

@@zeroej You have my respect

[@costineacsu373]

long live Lemmy Yeah. Me too

[@arturo6780]

Because al though this may teach the general idea of the lesson, it is when you are in class and put it into work in practice problems that you solidify the understanding of the lesson. Not only thru practice but also explaining it to your peers/classmates who may have learned a different way. Its like a gym for your brain!

[@arinjaytayde6617]

This is 11 years old video but still the animations and quality are up to date hats off

[@CresentX]

Wow TED-Ed, never quite understood the traditional expiation of log base 10 until now. Well done!

[@lexinaut]

Love the comic touch and vivid examples of real world uses. Logarithms have been called Napier's Rapier, since he invented them back in Elizabethan times to cut through difficult calculations precisely and quickly. This video makes you a true exponent of Napier.

[@PeaceCalm]

At last, I got it! Thanks for the education.

[@dannyu.4699]

Man, you are a legend. I read a book, listened to teachers and stuff, but this 3:33 long video explained what hours of learning couldn't. You are a LEGEND!

[@bobbluered8984]

This taught me more than a semester course in Pre-Calculus.

[@btdpro752]

Bob Bluered that's impossible unless you weren't paying attention

[@EverlastingLuigi]

I will still never remember logs

[@MegaMGstudios]

i had a test about them last week

[@wisdomcongeal2110]

Emilio Couchee soooooooooooo true

[@PokeMageTech]

Emilio Couchee Why? Cause random hunks of wood are boring?

[@vaizerdgrey]

Base raise to what power equal number.

[@alexthegreat7518]

REMEMBER Logs are bits of wood that are chopped from trees.

[@wailinaung4371]

Thanks for subtitling with Myanmar.🇲🇲 It's rare on KZbin.

[@t.naidoo2762]

Loving the energy and enthusiasm!!!

[@AdventureOfTravel]

This was a very helpful video. Anyone who didn't understand it, was not actually watching it, just playing on their phone or some other activity.

[@MrHsuLaoshi]

+Emanuel Balmus Or they didn't understand it because they were just lazy and/or refuse to learn the concept of logarithm instead of just looking for "how do I do it?" or "But there were no examples" or etc :) Trust me, I teach.

[@misbahshaikh4447]

I agree

[@panushalimbu]

Thanks ... I was using the calculator to do my maths hw and then I had the strangest urge to know about the log button

[@MegaMGstudios]

never had LOG before at school?

[@btdpro752]

MegaMGstudios kids are everywhere dude

[@TEDEd]

Great idea! Do you have a recommendation on someone who could create the lesson? Feel free to nominate someone on the TED-Ed website (ed.ted.com) under the "Get Involved" section. Thanks!

[@IWantToStayAtYourHouse]

5 years and noone replied or liked this comment

[@btdpro752]

10,000 subscribers without any videos yea

[@zenithperigee7442]

@TEDEd, I just wanted to say that for the "pH" example @2:30, since it is a "small value", that one could enter the equivalent in negative scientific/engineering notation. So -log(3.98x10^-9 = 8.4.... and -log(3.98x10^-8 = 7.4.... Ty for the video! ^_^

[@funanime7461]

11 years have passed

[@onkarkalpavriksha8676]

finally some practical use of log , my god it felt good understanding log again

[@TheVirtualArena24]

This 3 min video explained better what exactly log is about than my school.

[@getpoked2498]

third week in math, I was helped more by a 3minute video than 3 weeks in college. Fantastic.

[@DarkAsgaro]

Same here! I knew the formula, but somehow before this video I didnt really realize what it really means and why someone would use it. But by this video, I know it just shows how much you have to multiply a certain number (=the base) by itself, to get a particular other number!

[@lravikiran88]

did he say log can be used as eye drops

[@TheLimpCottonToeBook]

Instructions unclear. Tree stuck in eye.

[@jawadzaidi9148]

Its a metaphor by the way indian guy

[@SiddharthSingh-zd7ny]

Mohd Jawad hes kiddin dude.

[@jawadzaidi9148]

Siddharth Singh i don't think so he's indian and watching there is high probability he is damn serious

[@huntersikari]

he mean probably the hydrogen ion concentration or the pH that cause the eye redness..can be treated by using eye drops made by using the same technique in order to lower the pH of your eye that caused the redness. he probably means the concentration needed are so small that scientist use logarithm etc. to calculate the required concentration etc.

[@mayank0508]

the last bit was actually so good, especially the eye drop joke

[@somerandomdude-UWU]

Oh my god. How is this the best explanation video I have ever seen on youtube in my life.

[@randmayfield5695]

Back in college I took a microeconomics course which was taught in an auditorium that held 250 people. At about the third lecture it was apparent that the professor was teaching to a dozen or so students that had some familiarity with the topic, the other 200+ students of which I was one, were lost and left behind. I stuck with it and learned enough from the text to manage a C grade from taking the 12 exams. At semesters end, the number of students had dropped to less than 50 or so. When I took macroeconomics I had an outstanding professor who not only taught macro well but got those of us who didn't 'get' an understanding of micro caught up to speed at the same time. She was a super educator and I was glad to have taken her class.

[@kimchee94112]

American public high schools are preparation for failure. That dozen in class are from college prep schools, foreign students or the exceptional onces from American public high schools which would be walk in the park review for them. I knew foreign freshman students already had differential and Integral calculus and first college year physics. We are so screwed!

[@FEED_EZ]

Oh man! The way this educator explain his lesson with his unique way of talking... Recommended educator

[@pomeloyc]

This provides a clarification. Thank you!

[@dienvidbriedis1184]

- Timmy, what number is under cup now? - 10? - no, it is an orange. (laughter and applause from audience)

[@jebjim9391]

I have loved math my whole life and my teacher who covered Log's did a poor job so I never understood the fundamental of it. NOW I GET IT. It's pretty simple actually thank you !!!

[@saujanyapoudel8910]

1:34 don't listen to him. You can do logarithm to any base using the change of base formula. For example to compute log base 2 of 64 you can type in log(64)/log(2) and that gives us the correct answer of 6. Remember, log to the base 'b' of a number 'n' is equal to log(n)/log(b)

[@abd_rf]

3:05 that's exactly how I remembered it! It's a super cool trick and have helped me a lot!

[@wheresjohn1944]

super helpful with the lighting up of the variables when you were saying what goes to what. Makes identifying what easier. thank you :D

[@aarnelehti]

I had difficulties understanding logarithms in school, now years later this one three minute video explained what they actually are. Turns out that my teacher never actually explained what logarithms are, only how to use them, so it never felt intuitive.

[@davidguerin6142]

The most important use of logarithms was first to help in calculations: log(a+b) = log(a) x log(b) It means that with a little book, a list of logarithms of numbers, you can multiply them just by adding their logarithms, whereas multiplying by hands is long and hard. That's why logarithms were a revolution in science because they were "invented" or "discovered" at a time when there was no calculator. (Sorry for the long text, but it seems important to me)

[@FeindrplaysMC]

That is a misconception. It is actually log(a) + log(b) = log(a x b), not the other way around.

[@davidguerin6142]

Yes, sorry ! You are right

[@warri7948]

so by using log(a)+log(b)=log(a+b) im guessing people programmed logarithms via a recursive function (c++)?

[@iftakharahmed1821]

Bro youve done mistake actually it was log( a×b)= log a + log b

[@hungryfareasternslav1823]

What about log(abc) or log(a_1×a_2×a_3×...a_n)???

[@lilpixie.9653]

Thank you for explaining in under 5 minutes what all my university professors have failed to actually tell me in nearly 6 years. This was all I've wanted, and I'm going to put it on my wall so that I don't have to keep scouring the internet every time I do a lab report.

[@kopilkaiser8991]

Brilliant lesson and a great explanation on the topic. You've been able to simplify the logarithm topic very easily and the student will be able to understand it way better from you.

[@rric7]

Good Explanation.. My teachers did not teach these basics and would just ask us to reference the Log Tables (calculators where not available).. Honestly, I am still confused a bit.. If additional examples could be included with actual calculations, it would be helpful. (specially, Log base 3). Is there similar examples for Calculus.. I know that these are important, but my basics is bad in these..

[@advaitanair9127]

There’s a teacher known as “Eddie woo” on KZbin, they have a video explaining logarithms Here’s the link: kzbin.info/www/bejne/pKWliKWZl6abl7s

[@nicolesong6199]

Laaawwwgarithms.

[@robertdavealonzo]

Everyone: logarithm TED-Ed: looowgarithm

[@LivingLikeLu]

I was holding a cup of milk in one hand and a croissant in the other when the narrator said, "c'mon, use your fingers" (1:54). I started counting with him and dropped my croissant first, then I dropped my cup of milk and it broke and got all over the place.

[@Calculator.108]

Even my teachers couldn't have explained such a beautiful way ... thanks

[@valdas0]

I would have loved to see some interesting examples of the use of logarithms. For example it's possible to find how many digits does a number have then raised to some power. Then we take the log base 10 out of one digit number we get an answer which is less than 1(because log10=1). If we take log base 10 of two digit number we get a number which is less than 2 but greater or equal to one and so on. Let's find how many digits does 5^15 have: log(5^15)= 15*log5 ≈ 15*0.7 ≈ 10.5 Number has 11 digits

[@juliant1876]

The STAR math test kept asking me about logs (in 8th grade!) and I had no idea what it was talking about. Now I can at least get most of them right. :)

[@abatejc4465]

Don't care

[@ryanjbuchanan]

Very simple and awesome explanation!

[@maskiifolkznoskimask]

Needed a reminder to help my niece in her math class. Thank you guys🙏🏽

[@edwardmorris3453]

This is not the video you want playing when you're mouse suddenly stops working.

[@jonathanschossig1276]

Edward Morris Did your autocorrect also stop working?

[@edwardmorris3453]

No, it just means this video is so goddamn irritating I made a spelling mistake. Obviously. Jeez you asked a stupid question. Go away.

[@jonathanschossig1276]

Edward Morris TRIGGERED

[@davecullins1606]

Logarithms seemed like such a complex thing to me when I didn't understand them. Now I'm just like "WTF. WAS IT THIS SIMPLE ALL ALONG!??!" "What must 10 have in potency in order to equal the number to the right of it?"

[@MsSBVideos]

ZEro ZEro ZEro ZEro eight four LOAAAAGGGGarithms. Blah blah BLAW.

[@KevinSalim]

I saw u in another video of ted-ed lol the one about zeno's paradox

[@abinashpanda393]

@@KevinSalim Three Nine Eight

[@KevinSalim]

@@abinashpanda393 what does that mean?

[@abinashpanda393]

@@KevinSalim You need to learn logarithm AGAIN

[@stevenmael]

Good luck, youre gonna need it.

[@Jackcabbit]

Really quick version: A natural log is a log where the base is the number "e." e (intentionally not capitalized) is a number similar to pi in that it doesn't split up well, but it has some interesting properties. For more info the wikipedia pages do a good introduction to both e and natural log.

[@haroonsharif8411]

Thanks for extra info

[@nobodyknows5046]

I NEED LOGARITHM TO SAY THAAAAAAANK YOUUUUUUU TO YOUUUUUUUUUUU

[@keithdejervis]

This video made me cry. Sensational!

[@doszlopleonard6031]

This was amazingly explained

[@FKBRODIE]

Thank you so much Ted-Ed for clearing my concepts from this short video 💓💓💓💓💓

[@ankitdubey9310]

zero zero zero zero zero zero zero zero zero and zeroooooo 3 98 lol

[@BijouBakson]

thank you for keep it so short and simple. I understood within the first 45 seconds.

[@renebarnard7139]

Excellent explanation, as always very helpful! :)

[@lavishangel4069]

I need another ted-Ed video explaining this video

[@JoachimderZweite]

I really liked this. I got an A in my college Logarithms class in college but I don't remember a thing but this brought it "all" back (partly). With math, like languages, if you don't use it you loose it. A smart young person should really study math diligently, write perfect English and learn either German, Mandarin, French. Latin or Ancient Greek. The last two are like certificates of intelligence because no stupidos have Latin or Ancient Greek.

[@db112nl]

If you dont use it you loose it --> So go study a dead language. You must see the irony in that :)

[@JoachimderZweite]

db112nl "Dead languages" survive very well in Academia and among enthusiast. Hebrew was a dead language for 2000 years until the creation of the State of Israel. The term "dead language" is deceptive as it does not mean dead but not currently spoken. My university math professor told me he would rather have brilliant students of Latin and Ancient Greek with little or no mathematics to start the year because he knew that with such students he could make great mathematicians. To test yourself try reading a language you do not know with a good dictionary - not very difficult - and then try reading Cicero or Virgil or Homer with a dictionary and see how far you get. There is value in "dead stuff." Ironic - huh!

[@martind2520]

I feel that someone who talks about what "a smart young person should know" should really know the difference between "loose" and "lose".

[@randymartin9040]

fantastically simple explanation thank you

[@es-xz4pv]

When you’re failing add maths and have to resort to Ted education

[@jidnyashujadhav9020]

I am watching this video after 11 years but it helped me in my physics. So thanks.

[@arachnodev]

My eyes are red. Someone give me logeye drops.

[@Volcanic_Rave]

*stabs eye with a stick*

[@zazanya1]

Super helpful video. I never had anyone really explain what a log is, so thanks very much! On a side note, this guy should be a game show announcer.

[@IDcLuc]

welp, he lost me at 0:01

[@someonethatexists1119]

I saw a couple log questions on a test and I didn’t understand it, videos like these really help

[@learningElectronicsBing]

I never knew logarithms were useful to handle extremely small/large numbers... Thanks for the explanation!

[@vanhell966]

Thanks for the explanation. I always wondered whats log , this helped me.

[@BentoTran]

2024 anyone?

[@fadeshadow2431]

Yeah

[@umasrivastava2107]

Bro the comment are so old. It made me feel so young

[@Null1fied07]

​@@umasrivastava2107fr

[@parulsutariya2779]

I am from 2024

[@sarikakale3258]

Bro me

[@rossholst5315]

Question regarding logarithms…it appears by bringing down the exponents we might be losing some information… Such as with the formula x^2+y^2=1 … Then X^2=1-y^2 (-1)(x^2)=(y+1)(y-1) Then X^4=(y+1)(y+1)(y-1)(y-1) X^4=(y^2-1)^2 Ln(x^4)=Ln [(y^2-1)^2] Then 4 ln (x) = 2 ln (y^2-1) And Ln(x)=1/2 ln (y^2-1) e^ln(x)=e^(ln(y^2-1)^1/2) And X=(y^2-1)^1/2 But from the initial formula X=(1-y^2)^1/2 So we must have changed the domain for which the function was defined at some point correct? Because up until we drag the exponents down in front of the logarithm. The graph still generates a circle along with the hyperbola portion as well. The ending product just leave the hyperbola portion. And the starting equation just had the parabolic portion. Log portion had both…

[@nandaballabhpant9557]

Well, in Boltzmann,'s entropy formula why is the change in entropy given by the log instead of simply by a number? Anyone may please reply! Thanks

[@dexter2392]

The key property of logarithms is that log(a*b) = log(a) + log(b). Because entropy is an additive property, taking two systems with different entropy and combining them gives you an entropy that just adds them up: S = S1+S2. On the other hand, combining microstates of two systems looks like multiplication, since for each microstate the first can take on, the second system can be in any microstate, and they're independent. W = W1*W2. Therefore, a logarithm is the only function that makes those two properties consistent.

[@nandaballabhpant9557]

@@dexter2392 thanks a lot for so clear reply

[@edwinmariano5131]

Very simple easy to understand explanation.

[@musicalsilly]

"Zero Zero Zero Zero Zero.." HAHA! Sounds funnny when he does that!

[@rajamouryasimhareddy1478]

Wow 8 years ago

[@xEEEa7iu231]

Actually using a trait of logarithms, you can decide what base you want to be computed in calculators by inserting log b / log n with both bases being 10, b being the base you desire and n the number.

[@usernamesbeentaken]

When the lecturer speaks at 1.50 speed so you don't have to adjust the video playback multiplier. MVP

[@turtles10]

Llooooooooooooooooooooooooogarithms

[@horsearcher6350]

More like "longarithms"

[@locle8777]

Thank you TED-Ed and Steve Kelly for this amzing and useful video!

[@Prashant-ls3dd]

see we need this in schools... not some uncaring drones called "TEACHERS"

[@happydays6777]

Prashant Pathania edgy

[@antiantiderivative]

fellow confederate says the traitor

[@ElevenAce]

now it makes sense after so many years. thx.

[@danielobi7169]

lol zerow, zerow, zerow, zerow!!

[@ansyyxux]

THREE NINE EIGHT

[@dheerajjoshi6266]

Thankyou, sir. My eyes were feeling very itchy, but now I can use logarithm to fix them.

[@omargoodman2999]

"The log key on your calculator only does log_10." log_b(p) = ln(p) / ln(b)

[@ur.local.deuterium.atom.6974]

0:47 b=base, p=power, n=number

[@j.mcq.8418]

I'd like to see more of these from this guy but sometimes he speaks too quickly I think.

[@LifeLongArtist]

Started algorithms for CS class and they briefly went over logs and I was so confused since I never used them in hs. Great fix right here

[@toastet1337]

I usually love Ted and Ted-Ed but this video was more confusing than helping

[@expressthisout]

I second this

[@the44thchamber]

Agreed. I actually understand logs and found the video to be unnecessarily complex for curious beginners

[@PumpReactivationProject]

For me it was really helpful and explainatory

[@Bubbliiqs]

Omg he explained it so well. I literally asked my math teacher to make me understand the same math of logarithm 6 times and still didn’t get it and was too shy to ask again but this video really helped!!❤

[@一世无懮]

學校教的我聽懂了，怎麼感覺這裡說的比學校還複雜。 。。

[@prashantvicky]

Out of all the languages, I must confess that the Japanese language seems the most beautiful when written. It looks like some buildings. 😋

[@23681lucky]

Mr. Kelly, best teacher at St. Louis High School, going to miss you next year when I am at college

[@spatch3624]

LWAgarithm

[@bloodjam3005]

if you want to find the answer for instance a problem where for example 2^x = 8 we know from the video it that x = 3 but to take the to working it out you can't access the x any other way than using logs so if we do log2 both sides of this formula it looks like this log2(2^x) = log2(8) then we can take the x out because of some of the rules of logs x*log2(2) = log2(8) then divide by log2(2) and we have x=log2(8)/log2(8) which is x = 3/1 so you can work out some physics formulas using logs