The History of the Natural Logarithm - How was it discovered?

[@peterclancy3653]

Finally, after 72 years, someone explained “ where and how” about logs. Thank you so much!

[@tareksaid81]

Thanks for sharing Peter. I am really glad that you found the answer after all those years

[@TheEuclid26]

Haha! I'm 68 with an engineering background and I too have been waiting for this moment. Finally!

[@tareksaid81]

@@TheEuclid26 Such stories make me really happy. Thanks for sharing :)

[@bramilan]

I'm am an only 47yo engineer but feel the same. Thank you!

[@nommindymple6241]

64 and (by education) a mathematician. And I never knew this. Thanks.

[@samisiddiqi5411]

12:36 This is for my own reference. Hands down the best and most complete video on logarithms I've ever seen on KZbin. History and use included. I like it.

[@tareksaid81]

Thanks Sami, I am glad you liked it :)

[@tweedyburd007]

I think this is the best way to understand why the integral of 1/x is ln(x)

[@henadzyermakavets120]

This is how math should look in the books and schools. The history of a discovery explains it at the best level in the cleanest way. We need to learn ideas instead of remembering formulas and algorithms sometimes without understanding.

[@tareksaid81]

Thanks for the kind words, this is what I hoped the channel would achieve and I am so glad it is resonating

[@larrymorley2579]

We need to know both. We need to memorize the shortcuts but also the theory.

[@jaytravis2487]

I've been an enthusiastic math hobbyist for years now and I've watched hundreds if not thousands of hours of math lectures. This is one of the most concise and original math explorations I have ever seen. Thanks a million

[@tareksaid81]

Jay, this comment really touched me. From the bottom of my heart thank you. It really means a lot. Comments like yours really motivate me to keep going. I am so glad that you liked it and I hope you'd like future videos

[@nickxyzt]

I've been waiting for this explanation my whole life. I always wondered how on earth natural logarithms were invented before the discovery of calculus and the number e. This is the most outstanding video about logarithms ever. Well done!

[@tareksaid81]

wow.. I am really glad you found an answer and appreciate your kind words. It means a lot to me :)

[@ishfaqmath6059]

I have been teaching mathematics in Asia for about two decades and I highly recommend students to watch extraordinary efforts by you to give a logical insight to basic concepts! Highly appreciated and keep on unlocking the basic mathematical concepts as they are not really taught at high school and majority of students are unaware of them!

[@tareksaid81]

Thanks a lot for your kind word and your encouragement Ishfaq. I am really glad that you are recommending the videos to students and I hope you would like future videos too

[@PluetoeInc.]

bangladeshi math teacher?

[@vister6757]

Ya, it's very important to teach how math formula is discovered and what it means. I hate it when I have to just memorise any formula / data without really understanding the rationale behind the formula concept.

[@bhanuinani8142]

The best explanation I could ever come across. Brilliant way to teach. The graphics were simply superb.

[@ingGS]

Beautifully explained. I am glad KZbin recommended you, great video!

[@tareksaid81]

Thanks IngGS. I am glad you liked it

[@welingkartr416]

Yes, I second that. No one explained in school or college what it was all about. We simply went about calculating things, doing our sums like monkeys that just figured how to use calculators.

[@samueldeandrade8535]

This man probably is the absolute BEST math youtuber we never had.

[@jonasgunnarsson5747]

The slide-rule, which is a logarithmic ruler with sliding parts, is an alternative version of the logarithmic table that utilizes this effect of logarithm to transform between multiplication and addition or between division and subtraction. As mentioned in the video, people used logarithmic tables and slide-rules to do calculations, before electronic calculators were invented. My mind was blown away when my dad showed me a slide-rule and I thought we should be taught about this. Thank you for the video, showing how this was invented.

[@tareksaid81]

Thanks Jonas, I heard about the slide rule in the past but never used it. I didn't know how it worked until I did research for this video. I heard that some people still use it today and prefer it to calculators!!

[@pashi47]

I think the story-telling approach of explaining something complex like the natural log is very powerful and it should be done more regularly in schools. Well-done!

[@tareksaid81]

Thanks. I find that I don't fully understand a concept until I learn about its history, motivations, etc. and I agree regarding using this approach in schools

[@AndrewBlucher]

​@@tareksaid81 Yep. The Physics text book I had in high school in the early '70's took this approach and for me it worked well. Learning is about connecting information chunks.

[@tareksaid81]

@@AndrewBlucher That's interesting. I wonder why this approach is not used anymore (as far as I know)

[@ze_kangz932]

​@@tareksaid81I think it had to do with the nature of school creation. Schools were created to produce employable engineers en masse, who are able to understand basic maths like sum, products, exponents and logarithms and who obey to what they are being told(so less incentive to promote thinkers). I think that's the reason, but it's my theory though.

[@tareksaid81]

​@@ze_kangz932 I have a similar theory. That's why one of my favourite quotes, which is attributed to Mark Twain: "I have never let schooling interfere with my education"

[@matthewphares4588]

Bravo! One of the most enjoyable videos I’ve watched on KZbin. I think math would be easier to understand if first taught from the historical perspective of man progressing to president day.

[@tareksaid81]

I am really glad you enjoyed the video Matthew. I totally agree regarding understanding maths through history. Mathematical ideas usually start simple and intuitive, but over the years they get more and more abstract. While they are more powerful in the abstract form, they are also more difficult to understand

[@warchitect73]

check out Eddie Woo too, his videos are also great at explaining, though he doesn't go so much into history. still fun to watch.

[@snipelite94]

It's likely beyond the communication powers (har har) between teacher and schoolchildren But it DOES make far more sense, when you realise WHY the genius mathematicians were creating these math engines Maths is mostly taught parrot fashion and we're all taught multiplication (and logarithmic) tables and then given exercises to complete (or else!) It should be de riguer for all math lessons to make the boilerplate statement that logarithms were just quicker to calculate before electronic calculating machines were invented! Addendum: I remember reading about the human calculator service before WW2 When scientists at Los Alamos and universities had too much maths and too little time, they'd actually phone or snail mail a bunch of guys who would do the MENTAT heavy lifting for them!!

[@leapdrive]

@@tareksaid81 , it may have been called Natural Logarithm due to its derivation from an area under a hyperbole. Unlike other logarithms that can be artificially set such as the Common Logarithm of base ten or any arbitrary base.

[@prprssrinivasan7785]

All knowledge is best learned in historical context...

[@qelmnl]

You really deserve a bigger audience. What is fascinating in mathematics is the line of reasoning that mathematicians follow to arrive at a concept. More so when the reasoning is rooted in experience and application. This is true intellectual discovery, and unfortunately far too often omitted form math class. Thank you for this video, I enjoyed it a lot and immediately subscribed your channel. Looking forward to more videos from you!

[@tareksaid81]

Thanks, I am working on it. I totally agree and I think maths would be much easier to understand if it was taught from a historic perspective. The thing with maths though is that over time, concepts become more rigorous but at the same time they become more abstract. Maths education today focuses on teaching those abstract concepts as they are more rigorous. Thanks for the sub, I hope you will like future videos too

[@doctari1061]

Awesome. After 62 years you finally explained something I’ve used for my entire life without knowing where this thing came from of how it relates to anything else. Cheers

[@tareksaid81]

I am so glad that you have found the explanation. It really makes me so happy. Funnily, we didn't use logarithmic tables when I was at school as calculators were already available and accessible. It makes me reflect on how fast we have developed technologically in the last decades!!

[@nkbrahm6826]

Never had these insights about logarithm..by far the best video I have seen on you tube..thank you so much

[@tareksaid81]

Thanks, I am really glad you liked it and I really appreciate your feedback.

[@chibbi4608]

Incredible!! Truely fasinating. Please create more videos on maths and science. As someone who requires the entire story on a concept to fully understand it, your content is exactly what I need!! You are an amazing teacher, thank you Tarek. Looking forward to more videos!!

[@tareksaid81]

Thanks for your support and your kind words Chibbi. I really appreciate it. I am the same, I need the entire story to fully understand a concept. Without the entire story we only get to see the tip of the iceberg, we don't get to see the thinking process behind the concept, the challenges faced, the human element, the step by step process to finally arrive at the result. I am currently working on the history of calculus, hope you'll like it

[@horseloverfat6938]

@@tareksaid81 Strange isn't it, how people learn - Calculus (in school) was taught to me totally backwards, starting with limits and no historical context. This was way too abstract, I was completely lost and gave up on maths (which I had deeply loved) for a decade. I had to circle all the way around again - I was researching the origins of science in ancient Greek geometry and their philosophical concept of infinity when things started to come together. Reading about how Archimedes calculated pi through exhausting polygons was the "aha" moment for me - I finally "clicked" as to how (and later why) calculus worked.

[@tareksaid81]

@@horseloverfat6938 Totally. In the first 200 years of calculus limits were not in the picture. Actually calculus evolved exactly in the reverse order to the way it is taught today. It started with integrals, then with derivatives and limits were introduced much later. While I do think that it is important to learn about limits as a way to make calculus more rigorous, I really think that limits should be introduced after students develop an understanding of what calculus is and what it does. In fact this will be the topic of my first video about calculus. I will upload it asap.

[@iyannazarian866]

Words won’t do justice to how many time I got “wowed” by these great and powerful explanations! That’s 3b1b quality right there! You’re still at a 1000 subs, but remember me when you get that 100K ✌️

[@tareksaid81]

Oh!! Grant from 3b1b has been a massive inspiration for me and being even remotely compared to his work is a badge of honour. Thanks for your support and kind words Iyan and I would definitely remember you :)

[@user-yc3fw6vq5n]

Okay

[@user-yc3fw6vq5n]

at about 4,860 subs now

[@SajjadAliSuhag-q7c]

Over all one of the best and well organized lectures on the concerned topic 😊

[@curumo_curunir]

Teşekkürler. Thank you very much for the nice explanation and the video. I really liked the corrections and extended explanations in the description section. I think you have the talent to explain complex topics to the regular interested person. I am looking forward for more videos from your channel. Kind regards. Greetings from Turkiye.

[@cretkrat]

I'm currently studying engineering, I've been working with logarithms since at least a year and a little less than a month ago I have started to question myself "Where the f natural logarithm and the Euler's number come from?", "Why they have to be those exact numbers?" I didn't searched this video, the algorithm bring it to me and I couldn't be more glad about it. You finally answered my question and I didn't have to wait it for 50 years

[@tareksaid81]

I’m so glad the video helped. Actually I have a very similar story. I too studied engineering and asked this very same question. When I searched for an answer, I didn’t find one that satisfied me. So I thought the answer must be in history books and sure enough, it was :)

[@l-lsb2084]

I never comment under a video, because I believe my commemt can't add much to the conversation; but this time I must let you know: this is the best maths related video I've ever seen (and I've seen a lot!). You beautifully conveied the idea of what mathematics was like in its early stages, before widespread standardisation, when being a mathematician wasn't associated with rigor and stiffness, but rather mathematics was creative, imaginative and required a deep personal understanding of numbers (and it probably was even more different than I can imagine). This really gives an idea of how knoledge transforms through history and how we are boxed into the way of thinking predominant during our life. Many thanks for this piece of art! P.s. saved the video so I can watch it again when I'll have forgotten how great it is

[@tareksaid81]

Such a wonderful and touching comment. I really deeply appreciate it. I took a snapshot of it and shared it with family and friends :) Indeed, I like to think of mathematics as a creative, artistic pursuit. While I believe that rigour is important, there still should be place for intuition, both in teaching and in discovering new ideas. Over the last year, I've been researching the history of calculus, it is amazing how playful and risk taking (almost reckless) the pioneers were, particularly with the use of infinitesimals. Thank you, I feel more motivated to keep doing what I am doing!

[@LuaanTi]

Not only was this useful before calculators - many electrical calculators actually use logarithms for that too. It's extremely convenient and fast. And one of the big early motivations for creating computers (as in machines, rather than humans) was to make more accurate logarithmic tables, without the errors that often plagued the tables. It comes the whole way around :P Heck, some people still use logarithmic tables in their head for quick multiplication, division and all that :D

[@tareksaid81]

That's very interesting. I did not know that at all. That could become a topic for another video - logarithms in the age of computers :) The funny thing is that I did not know anything about logarithmic tables before researching this topic. It is funny how quickly they were forgotten, at least in the mainstream!

[@klam77]

You don't mention ......SLIDE RULERS!!!!! My dad used to own them!!!!!

[@howardebenstein3204]

​@@klam77 I am your dad. :)

[@klam77]

@@howardebenstein3204 Leather holster and all? with pocket clip option?

[@howardebenstein3204]

@@klam77 Leather holster of course! No pocket clip - don't think it was available. Anyway, unit was 10" long with more scales than a fish; no way it could be hung it from a pocket. Besides, I wasn't a total nerd :) I donated it (with case and documentation) to the Smithsonian a number of years ago; was living in DC at the time and just dropped it off. Got a nice letter and it's now in the National Museum of American History's collection of mathematical instruments as a backup. If you Google my name, Smithsonian and "slide rule" you can see photo and read about it.

[@fredspiessens2292]

Thanks! I think the exceptional quality of your presentation stems from the way you combine clear examples and explanations with the actual history of how/when things were discovered. That makes it so easy to understand that teachers all over the world should probably copy your approach.

[@tareksaid81]

Thanks Fred, I really appreciate your analysis as it gives me understanding of what's working and what I should focus on. Cheers :)

[@jeffbrunswick5511]

I wish people would teach maths like this, rather than rote learning techniques that enable you to pass an exam, but have no ability to resolve real world problems.

[@brendanquinn6894]

But if they do it this way everyone will be able to understand maths and not just the geeks and the socially backward kids! Everyone will be mathematically literate and we can't have that!

[@joeaverage8329]

Best explanation on logarithm I've seen on youtube. Please make more of these kinds of videos please!!

[@tareksaid81]

I'm really glad you liked it Joe. Sure, currently I am now working on a video about the history of calculus. Hope you will like it

[@joeaverage8329]

@@tareksaid81 Great news for me! Thank you for making these contents.

[@horseloverfat6938]

Totally awesome explanation. As an amateur, I have been teaching myself calculus via history & philosophy of science (my specialist field) and this video filled in a few more of the historical blank spots between Archimedes and Euler. This was clear, logical and concise - thanks so much!

[@tareksaid81]

Thanks. I am really glad you liked it, and I hope you will like my next video about calculus. Perhaps we can have a chat about it one day and bounce some ideas before I upload my next video?

[@horseloverfat6938]

@@tareksaid81 Hey sorry it has taken so long to get back to you. This is a really worthwhile project and I would really encourage you to keep going and publish some more material. Reading your comments, it seems so many people have found your approach illuminating and useful. That said, I know how hard it can be to devote time to side projects, so well done for even getting one video up here. If you would like to "bounce some ideas" that would be great. I'm always interested in where different teachers and writers choose to begin their calculus explanations. I will respond promptly, I promise. I'm not on social media, and I don't want to publish my email here - so can you suggest a way I can DM you with my contact email? Thanks again for your work

[@geonalugala]

Fantastic! It is amazing that I can now create logarithms of my own at home, accurately, instead of googling everything. Thank you for this history. Few, very few people could have explained what you just did. Genius mind, sir.

[@tareksaid81]

Thanks for your kind words Geo. I really appreciate it and it means a lot. I am glad you liked the video. My next video is going to be about the history of calculus. Hope you like that one too

[@techdoc99]

I really loved your video. I never knew the origins of logarithms and you presented it like a professional documentarian with a clear flow and examples. Excellent work!

[@tareksaid81]

Thanks for you kind words and support. I really appreciate it. I haven't thought about this in this light, but I guess you are right, it is a documentary afterall :)

[@malicksoumare370]

I always wonder how did they calculated the logarithms table... Definitely one of my favourite video of the year. Great job at explaining everything so easily...

[@tareksaid81]

Thanks Malick, I’m glad you liked it. I want to point out that this was only the first method to calculate logarithmic tables. After Napier’s logarithms, many different methods have been invented

[@mangojulie123]

I'm a math whiz and have been since a child. I used slide rules and log tables back in my day. And I also loved to teach. I love the way you broke it down into a teachable moment (well an 18 minute moment LOL). This is an amazing way to teach about exponents and roots. Regardless of the "base".

[@tareksaid81]

I am glad you liked the video. It is really interesting how quickly the slide rules were forgotten after introduction of calculators. When I was in school in the 80s and 90s, I didn't even know they existed!!

[@ajinkyakamat7053]

This is so beautiful. 10:37 was such an aha moment. Can't stop smiling and thinking about it. Watched the video like 2 hrs ago. Had to come back and leave this comment

[@tareksaid81]

I am really glad you decided to share this Ajinkya. I too couldn’t stop smiling when I learned about this

[@ainnovation6967]

Why only now I found you? I've been looking someone that explain where the heck this e came from. Thanks man. You filled the gap in my head that no one explained it simply about natural number. You triggered my kiddy mind and start to love Mathematics again.

[@tareksaid81]

That's great, I am so glad you found the video helpful and that it helped in reigniting your love for mathematics :)

[@stapler942]

Very well-written and demonstrated historical dive! An aside about the time between Napier and Euler: as I understand it, e as a number alone was first described by Bernoulli around 1685 as a compound interest problem, whose solution he gave as a series and estimated to be between 2.5 and 3. Not as precise as Euler's estimation, but it's interesting how many stages there were getting to the constant we know now.

[@tareksaid81]

Yes indeed, the number e was first discovered by Bernoulli but the link between it and the natural logarithm wasn't known at the time.

[@adrianyoung6919]

Excellent and insightful presentation - thank you Tarek

[@CaptainX24]

Really enjoyed the history lesson. When I was in high school first learning about Euler's number and the natural logarithm, I was fascinated by their connections and seemingly disparate definitions, especially since modern math can make their definitions a bit circular. It was nice to see this all explained, and I had never seen the proof of area under 1/x like this either.

[@tareksaid81]

I am really glad you enjoyed it. And I agree, the connections between mathematical concepts can get a bit too abstract and circular sometimes. I found that learning the history of mathematics clarifies a lot of those connections and concepts... I like to think of it as the longer yet more scenic route

[@marshallsweatherhiking1820]

Modern calculus/analysis text books often throw weird definitions at you without giving any intuitive motivation. It can be unsatisfying as the proofs almost seem to work backwards even if each step is logically valid.

[@tareksaid81]

@@marshallsweatherhiking1820 True. I believe it comes down to the tension between intuition and rigour. Text books value rigour more than intuition. While I do believe it is very important to develop a rigorous understanding of mathematical concepts and rely solely on intuition, I do believe at the same time that it is important to start with intuition and build a rigorous understanding later.

[@tillybillyboyboy]

This video frickin rules! I am seriously so stoked that such a concise and informative video on logarithms/the natural logarithim exists! Thank you for such excellent content❤❤❤

[@tareksaid81]

Thanks a lot for your nice words, I really appreciate it and it motivates me to keep going. Apologies about the late response. I have been off my channel for a while but now I am back on track :)

[@chiafohu6649]

Congratulations ! The first time the historical events of logarithm make sense to me

[@tareksaid81]

Thanks Chia, I am glad it made sense to you

[@grandlotus1]

Wow! You have no idea how bittersweet it is to rediscover that my brain can still (come close to) grasping this math some 5 decades after I last used it in college. Thanks!

[@tareksaid81]

That's really great Hugo. Thanks for sharing your experience. Hopefully it is more sweet than bitter :)

[@judesalles]

Wow. I watched this three times. What a beauty of an explanation. Thank you for the treat.

[@tareksaid81]

Jude, this is a very touching comment and I deeply appreciate it. When I was working on the video I wanted to share the sense of beauty I felt when I first learned about these concepts, not just the information. I am glad it came through. Thanks for sharing

[@marcelochan]

This 18 min video is an example of education logarithm, just made people learn faster and more efficiently. Well done!

[@tareksaid81]

Thanks Marcelo, I think stories and history take away from the abstractness of mathematics and make it more tangible

[@Onelemon1354]

Keep making these kind of videos please. Your explaination is beautiful

[@tareksaid81]

Thanks for your kind words. I really appreciate it

[@classical381]

I wish I could show this to all my classmates. Really out of the box teaching method. We think of math as just equations and sloving problems in school. I can appreciate math much more after learning this. Thanks for the series Mr Tarek Said. You're a great teacher.

[@tareksaid81]

Thanks, I really appreciate it. I believe that learning mathematics from a historic perspective makes it a lot easier to understand and a lot more tangible. Hopefully this approach will become standard at schools one day

[@pramodvora2067]

Tarek, just beautifully explained! Your explanation is just amazing! Thanks.

[@tareksaid81]

Thanks Pramod. I am glad you like it :)

[@ПётрПроценко-б3к]

Now I understand my father(85) and he's trouble in understanding logarithms! Thanks God I can share this enlightenment with a man himself!

[@tareksaid81]

Thats great and I hope your father will find the video helpful and please let me know if you, or him has any questions

[@dahleno2014]

I love this. I’m very interested in the history of math and physics. I think the process is beautiful and can help share an insight into how various things were found.

[@tareksaid81]

Thanks Dahlen. Very much appreciated. The aim of this channel is to focus on the history of different ideas and how they came to be. Currently working on the history of calculus. I hope you will like it

[@yurisich]

I agree. Especially with the last 150 years, this technique really helps tame the concepts into something mortals might actually understand. You'd be surprised how much knowledge came about trying to make radar work better in the 1940s.

[@sphakamisozondi]

You and me both. Also, checkout Kathy loves physics and history.

[@longhealthyjoyfullife]

I loved your explanation. Thanks for taking the time to do the research and producing this video. I just became a fan of your channel. Great job.

[@tareksaid81]

Thanks for your nice words. I really appreciate it and I’m glad that you have liked my channel. I hope you would like future videos too :)

[@longhealthyjoyfullife]

@tareksaid81 Yes, I am looking forward to your next video. Excellent content 👌

[@kip4393]

Mr. Said is a true storyteller: recounting history, teaching math, and somehow making the whole experience exciting at the same time! Thank you Mr. Said, I finally understand what a logarithm is.

[@tareksaid81]

Thanks for your kind words and I am glad you now understand logarithms :)

[@TonyAbbeyFETraining]

Beautiful explanation! As one who used log tables in high school and slide rules in industry I can totally relate to the disconnect with the equation form.

[@tareksaid81]

You can find some information at the following website: www.17centurymaths.com/ it requires some digging but it does talk about his shortcut. I hope that helps

[@fernandogomez8030]

After watching this, I am forced to display my admiration towards you and your work. This video is a wonderful explanation of a topic that we use constantly in high school but we are never explained anything about. I'm very glad I got it recommend because it has taught me something really interesting that I think everybody (especially those interested in math) should know. Can't wait for you to upload more videos, because they are really high quality and well explained, keep up the good work!

[@tareksaid81]

Thanks for your support Fernando. It really means a lot. I am so glad you liked it and that you took the time to write this. Comment like yours motivate me to keep going. I remember when I was at school and we were introduced to the natural logarithm I kept asking: "but why?" I didn't get a satisfying answer at the time! I hope you will like the next video. It will be on the history of calculus. Thanks again :)

[@fernandogomez8030]

@@tareksaid81 I agree with you, this is the most satisfying answer I've ever seen in regards to what a logarithm actually is, and I find quite funny that It didn't have anything to do with exponents, but our teacher always tells us: logarithm is synonym of exponential. Anyway, I'm really looking forward to seeing that video, the history of calculus seems really interesting.

[@tareksaid81]

@@fernandogomez8030 Thanks Fernando. Calculus has a much longer and intricate history so I am currently working on how to make it concise without losing its richness. I hope you will like it :)

[@balkanleopard9728]

Brilliant. I'm coming back to pure maths after nearly 50 years as an engineer - and it's a marvellous feeling. Thank you. Keep it coming.

[@californiadreamin8423]

I needed the fantastic explanation 55 years when studying A level maths !!

[@tareksaid81]

Thanks California Dreamin'. Comments like yours motivate me to keep going :)

[@herq2409]

I really enjoy the way you teach - concepts are introduced one at a time, explaining each step. Your visuals are simple and clear, with no extraneous information. Great job! Subscribed because you're awesome! I appreciate ya!

[@tareksaid81]

Thanks for the nice words. I really appreciate it and I am glad you liked the way I teach. Thanks for the subscription too. I hope you would enjoy future videos as well :)

[@Etevoldo]

The quality of the video is overall amazing, I can see a bright future on this channel, just as I am looking forward on future videos!! History videos on math and physics is surprisingly scarce on youtube, and I'm so glad you're planning on filling it!!

[@tareksaid81]

Thanks for your kind words and encouragement. And yes you are totally right, it is surprising how few history videos about maths and physics are on KZbin. I am working on it :)

[@husniolama8283]

As students, we are, usually taught maths and physics with heavy emphasis on "how," that is how to plug-in numbers into the formula, and a lighter emphasis on "what." Almost never were we told about "why." After 41 years of being an Engineer, I finally understood why "log" and "ln" are used. Thank you Tarek Said.

[@tareksaid81]

That has been my issue with the way things are taught too. I always wanted to know the why before the how or the what. I later found that the best way to get an answer to the why question is by learning about the history of the topic. Thanks Husni and I am glad this video provided an answer for you :)

[@danibarack552]

Really interesting, the way people int the past thought about logarithms is so different from what we know now. I'm glad someone thought to cover this topic! However, I think you could have expanded a bit more on how people got from the hyperbolic logarithm to understanding that it has links to exponentials.

[@tareksaid81]

Thanks Daniel, I really appreciate your feedback. The original plan was to talk about how the connection of logarithms with exponentials was discovered but then I realised that it would probably be another 20 minutes and thought that the video might get too long. Perhaps I will do a future video about it.

[@purpleparadise2001]

Im glad that youtube recommended this video to me

[@tareksaid81]

Thanks. I am glad you found it :)

[@TheManzico]

@@tareksaid81where are you?? I am a subscriber to your Patreon. Hope you are keeping well? I am so looking forward to your video explanations!!!

[@MegaSquiff]

A truly excellent explanation….right up there with the very best. I agree completely with the viewer who said the historic lead-up approach is the ideal way to explain a math concept. A big thanks and subscribed with attitude!..take care…

[@tareksaid81]

Thanks for your kind words and I’m really glad you found it helpful. And I agree, it’s usually a lot easier to understand concepts by learning about their history. I’m currently working on the history of calculus which is a lot longer so I decided to make it into a series. Episode 1 has already been uploaded. I tried to make it generic as it is just the start. Thanks for the sub. Hope you’ll like future videos :)

[@ColonelDecker001]

Really very impressive Tarek. So many youtube sites repeat the laws but don't fundamentally understand the history. A real pleasure to watch and listen to someone who knows what is actually happening.

[@tareksaid81]

Thanks, I really appreciate your comment and I am glad you liked the video. I found that when I want to deeply understand any topic I have to read about its history hence the motivation for this channel. I hope you will like future videos too :)

[@Zicozaki]

Great and clear explanation, thanks so much, well done Mr. Tarek.

[@tareksaid81]

Thanks. My pleasure Mr. Zico :)

[@adarsharao8957]

After 27 years after getting introduced to logarithms, today I understood how they really work. Thanks a lot for very beautiful explanation.

[@tareksaid81]

I am glad you found this video helpful and thanks for your kind words :)

[@tameryazji1017]

Amazing explanation in a very nice simple way, I loved it! Thank you

[@tareksaid81]

Thanks Tamer, glad you liked it

[@muhammadjalal2335]

@@tareksaid81 hii

[@jaylenoschin8189]

brilliant, these types of videos are why I love KZbin. Thank you!

[@BacemAlafandi1981]

Great idea to explain math in this way, I really appreciate your effort 👌

[@tareksaid81]

Thanks Bacem. Your support is much appreciated

[@TrussttN01]

Best explanation I have ever had of natural logarithms. Math instructors would do well to play this video for their students as they introduce natural logarithms.

[@tareksaid81]

Thanks. I am really glad you found this explanation helpful

[@ayhamfawakherji716]

It is nice to know the hidden stories behind those equations.

[@markhughes7927]

Really quite astonishing! Walks in one door of a hall of history and four halls and 100 years later comes out in another! Thanks so much!

[@tareksaid81]

Thanks Mark. I’m glad you liked it and I really like your poetic description :)

[@vynderma]

Great explanation. I'm always looking for multiple views to improve my understanding. One of my favorite books about math is " e The story of a Number" by Eli Maor.

[@chocolatemodelsofficial5859]

You are an amazing teacher. I would love to watch more of these type of videos from you..... but I know KZbin is a lot of work. Thanks for these 4 gems.

[@ShijuAlex]

Beautiful explanation. The way you explain with examples is extraordinary. That is helping us to grasp the topic easily. ❤ Thanks to youtube also for suggesting this video. 😊

[@tareksaid81]

I am glad you liked the video and thanks for your kind words. I really appreciate it :)

[@touzaikokon]

been trying to get logs to "click" for years and your rundown of the how, what, and why make me feel a large step closer to that. thank you

[@tareksaid81]

I am really glad it helped you better understand logarithms. In modern use, logarithm are not used for calculation anymore, however they are used in certain scales, like the Richter and decible scales. Please feel free to ask me any questions you have about them

[@Notthatkindofdr]

Extremely clear explanation of the natural logarithm and its history! The excellent graphics are just the right amount of detail. I will share this link with my calculus class!

[@tareksaid81]

Thanks for the feedback Wayne, I really appreciate it and I hope your calculus class would find it useful too. Cheers :)

[@bignamek]

I’ll be honest, this is probably the best explanation of _e_ I’ve ever seen. Great video!

[@tareksaid81]

Thanks. I’m glad you liked it:)

[@marklama6435]

This is absolutely fantastic! I have been searching for a way to motivate the natural logarithm for my pre-calculus class, and after watching videos from other prominent math KZbinrs, I am sold on your historical approach. You are crystal clear!

[@tareksaid81]

Thanks... I am so glad you found the historical approach helpful and that you will be using it in teaching. I hope your students like it too. I remember when I first learned about the natural logarithm in high school, I kept asking "but why?" You didn't want to be my teacher then :)

[@hippopotamus6765]

Simply the best! Making a complex subject comprehensible.

[@tareksaid81]

Thanks for your support. I am glad you liked it

[@edwardsteen3058]

One of the coolest things I've seen in a long time. Thanks!

[@gatemanway]

Clarity, what a rare commodity. You are gonna be huge in KZbin. Suscribed and hungry for more!

[@tareksaid81]

Your comment really touched me gatemanway. Thanks :)

[@dmurphydrtc]

Well done. Best video on Logs that I have come across on utube.

[@tareksaid81]

Thanks David. I'm really glad you liked it

[@offgrid-bound]

What a joy! When you showed the geometric and arithmetic progression in a table, it was so obvious! Even though I understand this relationship very well (I used to use a slide ruler in high school to perform multiplications and exponential calculations), I have never seen it in such a simple explanation.

[@tareksaid81]

Thanks for your kind words, I really appreciate it and I am glad you found the explanation simple. I hope you find my other videos easy to understand too

[@21ruevictorhugo]

I’m so glad to see this video. Back in the Stone Age, when I was in high school and learning about logarithms. We learned that they were the way to make multiplication of large numbers easy. I remember exactly where the logarithm book was in the library, where I did homework. There were no calculators back then either!

[@tareksaid81]

That's really fascinating. When I was in high school, calculators were already very common and we studied logarithms only as inverse functions of exponentials. I had no idea at the time that only a decade or two earlier they were still very much in use!

[@algorithminc.8850]

I think this is about the best coverage of this topic that I've ever seen. I like the story/history aspect to set context/origin. Great work here. Subscribed. Cheers

[@tareksaid81]

Thanks, I really appreciate it. I personally find that looking into the history of the development of ideas makes them a lot easier to understand

[@prototropo]

Thank you for following each assertion with an example! So many instructors, engineers, mathematicians, etc, simply rattle off the equation or axiom of regard and don't demonstrate the practicality, or sample function in the real world. This video really made sense because of example we might actually encounter.

[@tareksaid81]

Thanks Denny, I always found that I won't fully understand a concept until I see some of its applications, so I made sure that I do the same in my videos. I am glad you found this approach useful

[@SurgInnovatioNow]

Thank you, Tarek for your very understandable description of logarithms. The history of the subject is most illuminating.

[@tareksaid81]

Thanks, I am glad you liked it :)

[@jemeaoo7713]

This is good. Thank you for your efforts

[@net51cc]

This video has answered many of the questions I had about natural logarithms. Thanks!

[@tareksaid81]

I am really glad it did. My pleasure :)

[@thefunpolice]

This and Mathologer's video on logarithms are both spectacular, complementary videos. A superb upload, Tarek. Thank you.

[@tareksaid81]

Thanks, I really appreciate it. I am not sure I watched the Mathologer's video. I will check it out

[@jimmygravitt1048]

Oh my god. You are blowing my mind right now. I am not even halfway through, yet and you have already helped me to understand more about logarithms than several hours or reading and other videos. Subscribed.

[@tareksaid81]

Thanks, I am really glad you liked the video

[@furey1]

What a fantastic video about logarithms. Thank you!

[@Pk_Ok_Oo]

thank you for an excellent video. I'm recalling my secondary school, and nautical science studies, and finally its starting to make sense.

[@RalphDratman]

Excellent! I learned several things I did not already know -- and I am 70 years old and have enjoyed mathematics for most of my life.

[@tareksaid81]

Thanks Ralph, I am really glad that you found new things in this video. You encouraged me to keep looking for not very common knowledge in future videos. Hope you will like them too :)

[@Higgsinophysics]

Such a brilliant way to explain the concept... Thank you

[@osvaldocristo]

OMG! It took more than 45 years since I learned Logarithm Theory to get answer to some questions I never got answered previously. Thank you very much!

[@tareksaid81]

Thanks Osvaldo. I am really glad that this video answered questions for you. Hope my next video, about the history of calculus, will answer some more questions too :)

[@ShaneIsNotMyName]

Thank you, it is a fantastic video. as I searched, you are the first one who made this clear explanation of natural logarithm on the internet. It is much better than those who talk about natural population growth.

[@tareksaid81]

Thanks, I am glad you liked it. Like you, I found the explanation using the natural population growth not very satisfying as it doesn't explain why the base of the natural logarithm is the number e. So I did some research into the history of the natural logarithm and thought it is worth making a video about it

[@KevinBalch-dt8ot]

This was the best explanations of logarithms I have ever heard! Subscribed.

[@sarathi1638]

Brilliantly explained

[@berniecsx4556]

I have wondered where e came from for decades, so good to finally get an answer. Thank you.

[@tareksaid81]

You are welcome :) I am glad you found that answer eventually

[@Jose_814]

You are my sunshine My only sunshine You make me happy When skies are gray You'll never know, dear How much I love you Please don't take My sunshine away

[@artscience9981]

Wonderful explanation of the natural log and Euler’s number! I always wondered where those came from!

[@tareksaid81]

Thanks. I am glad you found the video helpful

[@drmichaelshea]

Thank you. Very instructive.

[@mikegenco9646]

Everybody pretends to know where e came from but almost everybody does not. I had calculus 1 in 1972 and eventually made it to partial differential equations like many engineers but never knew where e came from. Thankyou so much. Perhaps a better way to teach math is from a historic perspective which keeps it grounded in practicality. Please make more videos with about a 10 minute duration for each and playlists by topic. Always remember that a lot of people view them on a smart phone. Great work.

[@tareksaid81]

Thanks Mike, I also didn't know where e came from until I started learning about its history. I agree, learning mathematics from a historical perspective makes it much easier. Regarding the length of the videos, the plan is always to keep them as short as possible but at the same time I aim at making sure that the story flows

[@vishwasmokashi3380]

Thank you, I am an engineer, and we were never explained Integration, Derivatives and Logarithms the way you explained. I am sure it is not explained now too. We were just mugging up and following steps, without understanding it. Exams were more important. Thank you so much Tarek.

[@tareksaid81]

Thanks, I am an engineer too and it wasn't explained this way when I was studying engineering either. Before I worked on the video, I wanted to understand the natural logarithm on a deeper level so I read different methods and found that the historical method was the most illuminating way. I am glad you liked it :)