Logarithms: why do they even exist?

[@HuxleyCrimson]

I think it's safe to say many of us feel the reason this topic is often disliked stems from the lack of context in schools and universities. As an engineering graduate, I found myself relearning almost everything independently to truly grasp the subject, rather than just focusing on passing exams. Fortunately, I now have the time to access resources like yours, which were not available when I was in school. Libraries were (and still are) filled with dry, context-lacking textbooks that made learning challenging. In response, I've started teaching to provide a different approach, and it's satisfying to see that everyone can succeed when taught the right way. Your content is truly valuable, and we wish we had more teachers like you.

[@ciaranmcevoy9875]

Your story sounds awfully familiar to mine :) thanks for the lovely comment

[@Lleruelu]

I love mathematical explanations that include historical context. Those help me to understand the purpose behind the tool, and suddenly all feels much more down to earth. Thanks for this awesome content!

[@ciaranmcevoy9875]

You're very welcome, I'm so glad it helped you. Thanks for the lovely comment!

[@chakrameste]

Had a math teacher from the 5th to the 9th grade, that always introduced new contents with the history behind them. Who invented it, when did it started being used, what are the uses in the real world... It captivated the attention of the class and made math a lot more interesting. It went from the most hated class, to a passion that I still have today. She was a great teacher. I actually spent 4 years teaching when I came out of college, and I tried to apply that same method as much as I could.

[@normanklein3155]

@@chakrameste I never took your class, but would still like to thank you for providing this service to your students. I just wish that I had been one of your students as knowing the historical context is the only way that I can really learn and understand mathematics. I remember always asking my teacher "Yes, but why do I care?" and being told "because it's going to be on the test".

[@samdev9147]

I'm a product manager trying to understand why our math expert has inserted log base 10 in a formula. I still don't understand that but I understand logs much better than before. Thanks for this!

[@ciaranmcevoy9875]

You're welcome Sam! Glad logs are making more sense to you now.

[@histrion2]

What's the formula?

[@torshavnnewell]

​@@histrion2 probably a trade secret

[@Bapuji42]

How about asking your math expert? I bet he knows.

[@frater_niram]

He probs just wanted to compress datasize in db, number's sizes may be capped depending on which u use

[@josephnardone1250]

Are you aware of why Napier wrote his work in Latin? At that time, Latin was the universal language of educated people. Whether spoken or written, an educated person from one country who did not speak or write the language of another educated person from another country could communicate with that person through Latin. Since Latin was a dead language, it meant that it was unlikely to change. It also meant that if a person wanted to attend a college in another country, he didn't have to learn the language of the country the college was located in. That is why Latin and Greek are stil used in science today.

[@ciaranmcevoy9875]

That's brilliant! Thanks for sharing!

[@Bapuji42]

What about pig Latin?

[@Nivleknosnhoj]

The more I learn about the past the more convinced that we have past a point of inflection in homosapien evolution and are now progressively becoming stupider with respect to time I become.

[@Bapuji42]

@@Nivleknosnhoj I agree. p.s. "past" should be "passed" and I would move "I become" to just after "more convinced".

[@Nivleknosnhoj]

@@Bapuji42 I'll pass 😆

[@josephcassano6296]

Logarithms are one of the most amazing mathematical tools that I have come across so far in my studies as an aspiring engineer. Math is used to define and logarithms give us the ability to make definition of that which we usually cannot do algebraically. They can help us to better understand the world around us and give are a tool to precisely find that which we instinctively estimate as human beings. One thing I really love about logarithms is their function in finding the distance between things, measuring parts of a whole, whether it be music, sound, something physical, and so on.

[@ciaranmcevoy9875]

Thanks for sharing your insight Joseph. Great to hear such passion and interest!

[@draftplus]

Following your introduction, I asked myself "what kind of oddity am I ?" because I really wanted to know what a logarithm is and what is it used for. I passed all the mathematics courses for a career in mechanical engineering before computers, and even calculators, but never digested the content. Just passed. This video is exactly what I was looking for. It is the amazing minds of the heroes of mathematics that I would like a piece of. Today, computers have left humans without a reason to think, understand and consider applications. No engineer I work with remembers a course taken. They rely on apps with no idea what the app is doing. God help us when the electricity ends. ...Now, off to a video on how to use my fathers slide rule.

[@SeymourSunshine]

"Today, computers have left humans without a reason to think, understand and consider " I'm not sure that I agree with this. It might be true for a large number of people, but not for the scientists and engineers who are creating the future. And I think this has been the case throughout history. It's those with (I) an insatiable curiosity and (ii) the ability to understand complex ideas that drive the bus; the rest of us are just passengers.

[@melizabethwoaini3262]

Great video! I finally understood what " Log " is for!!!! plus the background story of how they came about made it interesting and extra easier to kinda grasp.

[@ciaranmcevoy9875]

That's great to hear Melizabeth! Glad you enjoyed the video.

[@jean-jacquescharlet5296]

Hi Congratulations from the French Alps. I love your story telling about logarithmes. I had two challenges while watching your video. The language and the maths. I am getting better at both because of you. Not kidding. Keep on doing videos of such quality. All the best cheers. third challenge was typing in English.

[@Parapresdokian]

Man, I hate math but this one right here has changed by perception. And Laplace's praise got me goosebumps. Thanx, earned a sub!

[@ciaranmcevoy9875]

I really appreciate that Narendra. Thanks for the lovely comment!

[@EvilSandwich]

I'm legitimately shocked that not once was William Oughtred brought up. The man who single-handedly took the "OP plz nerf" logarithmic property of log(a)+log(b)=log(ab) and used it to create the slide rule. A computational device so incredibly useful, revolutionary, powerful and groundbreaking, that it was in continued use for over 400 straight years and it took literally the invention of the electronic calculator in the 1970s to finally surpass it. Logarithms literally put Buzz Aldrin on the moon with his landing calculations that he computed on his Pickett N600-ES Trig Log Log pocket slide rule. A feat that would have been impossible without Napier's hard work. :D

[@ciaranmcevoy9875]

The "OP plz nerf" property hahah love it! Great addition thank you! The main focus for this video was how logs were invented so I didn't end up talking about the slide rule. Might do another video on that invention alone.

[@EvilSandwich]

@@ciaranmcevoy9875 The Change of Base formula is also pretty broken, not going to lie. "Oh, crap! I need to find the log of some strange base but my calculator only supports common log and natural log!" *Change of Base formula busts in like the Kool-Aid Man*

[@givenfirstnamefamilyfirstn3935]

My school slide rule is my oldest and one of my most valued possessions. Teacher wouldn’t explain the LL exponential scales and they were not at all intuitive to use. I learned how to use all of that slide rule forty years later with the free time approaching my twilight years.

[@Apollo_Dionysus_Hermes]

But what exactly is a logarithim? What does it do to the number, I don't quite understand still. How did they figure out how to use logarithims, how does it modify the number? I'm deeply confused, but highly intrigued!

[@MegaSquiff]

Very interesting and well presented in a clear voiced…subscribed!

[@ciaranmcevoy9875]

Great to hear pal! Glad you enjoyed it.

[@ronan5946]

I am a game developer trying to understand where Logarithms fit in this area. It's a pretty interesting topic! I am still struggling to grasp it's pure essence. Something is still missing. But, great video! One of the best I've seen so far.

[@APaleDot]

Well the pure essence of logarithms is that they are the inverse of exponential functions. But that just begs the question: "what is the pure essence of an exponential function?" Maybe these two answers to this question will help you (if you don't already know them): 1) Exponentials are functions that convert addition of their inputs into multiplication of their outputs. To take the inverse, we reverse the input and the output. So the upshot for logarithms is that they are functions that convert multiplication of their inputs to addition of their outputs. 2) Exponentials are functions that grow in proportion to themselves. In other words, the rate of change at some input is just the output of the exponential multiplied by some constant number. Once again, to find the inverse we reverse the input and the output. So the rate of change switches from dy/dx to dx/dy, which is the reciprocal. This means the rate of change of the inverse is some number _divided_ by the output of the exponential. But remember the output of the exponential has become the input of the inverse function! So, the rate of change of a logarithm is simply some number divided by its input. These two interpretations cover a large portion of the properties of logarithms.

[@KipIngram]

Do you remember learning in school that you can add exponents when you multiply? As in, x^a times x^b is x^(a+b)? Well, that's all logarithms are. If y = b^L, then L is the "base b log" of y. 10 is the most obvious value for b - those are called common logarithms. But there's also a special number called e - those are "natural logarithms." And if you happen to work in computers or information theory you might see 2 used as the base. The whole idea is that this lets you directly exploit the "adding of exponents" to turn multiplication problems into addition problems. Computers hide the value of this, since it's just as easy to type * as it is to type +. But addition is faster on computers than multiplication, so in the game arena you might find occasional places where considering logarithms might let you produce faster code.

[@vincentgayle9954]

what a delightful explanation of why our perception of time changes as we get older, thanks.l

[@DigitalMirrorComputing]

Not only are you incredibly knowledgeable and engaging you are also funny, charismatic and an incredible story seller communicator. Bravo! Subbed!

[@therealdisston]

Finally, a mathematician that speaks coherently. Subscribed.

[@ciaranmcevoy9875]

That's great to hear pal!

[@therealdisston]

@@ciaranmcevoy9875 I meant to say something along the line of you are aware of the meaning of what you are saying. That comes through to your audience.

[@ciaranmcevoy9875]

Thanks pal, I appreciate that.

[@michaeldeburgh2173]

I think you've done a fine job with this. Napier's logarithms and Harrison's clocks are two British ideas that made marine navigation much easier and saved countless lives at sea.

[@GROG-l7g]

Absolutely fantastic! I need to learn math with the history and reason it was discovered. Overjoyed to be a new subscriber, thank you!

[@Jamesloh-o8t]

Thank you for a light introduction to a topic that has me puzzled me for a long time

[@spencerbentley8852]

As pitches go, "If you can't survive without seeing my face, subscribe" is defiantly.... one of them. Made me giggle, so Subbed anyway!

[@ciaranmcevoy9875]

Glad it made you giggle

[@justsomenightowl7220]

You know, I did not believe you when you said I might even start to like logarithms by the end of the video. Well, I have successfully been proven wrong 😂Thank you so much for this! You had me hooked the whole video (plus I love your sense of humour tactfully sprinkled in) and made a topic I hate so interesting. Fascinating story, huge respect for John Napier and the others. Just wow

[@ciaranmcevoy9875]

Haha that's brilliant to hear pal! Thanks for the lovely compliment.

[@sinanayenigul8731]

It might have been tough to research and write maybe, but the way you convey it to the audience is even more impressive considering you do it like a conversation or a stand--up. Great video.

[@ciaranmcevoy9875]

Thanks pal. That's very kind of you to say.

[@someonespadre]

I came into possessive of a book of 7 place logarithms from 1 to 100,000. I’ve used them to convert complicated calculations into nothing but pencil and paper. Also found logarithmic trig functions, they are log+10 to avoid negative numbers.

[@ciaranmcevoy9875]

Love that! Using logs for their original purpose. Nice.

[@ericlipps9459]

I wrote a Visual Basic function capable of taking logarithms in either base 10 or base e. It used square roots and was surprisingly short. (I also wrote an inverse function to extract numbers from their logs in either base.)

[@PinkeySuavo]

08:25 I feel like some example would be nice, I am not sure if I understood how they could calculate any numbers. But so far the video is very interesting!

[@ukasz6074]

exactly! I was missing that too

[@allanwrobel6607]

Entertaining, accessible and informative all in one video - I'm subscribed. (Natural Logs are built into the universe, there not going away)

[@kavalkid1]

I appreciate and admire your benevolence.

[@glyakk]

I am not a mathematician. I am just a self taught software developer who is struggling though a computer science course. One concept I keep running into is logarithms. Finding information on how to use them has been straightforward, but felt like only half the story. I wanted to know why they were even a concept. I knew they were useful, but I did not know what problem it was meant to solve. It felt like they only existed just for the sake of being esoteric so problems could be solved in a specific way. To my mind they were a solution searching for a problem. It just felt like an alternate way to write exponential equations. Your video does a wonderful job at starting to help me understand they are indeed vital to understand and not needlessly esoteric at all. Thank you!

[@ciaranmcevoy9875]

That's great to hear pal. Glad it helped!

[@ianthehunter3532]

do you still have that poster link?

[@tomboytomgirl5356]

Thanks Ciaran! You've added a lot of fascinating history of these peculiar functions. I love it!

[@ciaranmcevoy9875]

Cheers Tommie, I appreciate that pal.

[@whatzause]

Thank you! Taking on the task of preparing and teaching about logs proves you have a lot of stamina. Use that while you have your youth and I will look forward to more lessons. A note: I once told an experienced engineer (who was always somehow confused by logarithms) Repeat, to yourself, “A logarithm is an exponent.” (of a base.) After that he was confused no longer.

[@ciaranmcevoy9875]

Thanks Zack!

[@iguana1677]

Fascinating. I never knew their basis or history. I understand them much better now. Thank you!

[@ciaranmcevoy9875]

You're welcome Ron. Glad you enjoyed the video!

[@fernandodoldan2864]

Fantastic video! It was super engaging, well-researched and just lovely to watch. This is no small feat with a subject as potentially dry as logarithms, but you made it come to life like few ever could. Hats off to you sir 👍🏼😊

[@ciaranmcevoy9875]

Thanks very much Fernando. What a lovely compliment. I appreciate you acknowledging the difficulty of the subject, so it really is great to know that it came across that well. Thanks again pal 🍻

[@slmyshell]

The years being just as long as they ever were is exactly what I needed to hear. Thank you!

[@ciaranmcevoy9875]

Hey simyshell, glad you found some comfort in it, as did I.

[@wlhgmk]

Logarithms allow the solving of some sticky equations. For instance the radioactive formula. It depends on a log identity. Namely the log to the base a of b raised to the power of c is equal to c times the log to the base a of b. In other words you can put the exponent before the log expression instead of leaving it as an exponent. By the way, the radioactive formula is At = (1/2)(t/h)A0 You can't reproduce exponents and subscrips here so in words: The amount of a radioactive substance at time 't' is equal to one half raised to the 't' divided by h times the amount at time zero where t is the time elapsed and h is the half life of the particular isotope.

[@crimfan]

Historical context helps a ton! Logs are still super important in computation. Lots of computations are done on log scale and only turned back to normal scale at the end. If you don't, you frequently overflow the computer and can induce other numerical issues. As an example, if you work with the gamma function, chances are very good that it's actually represented internally as the log-gamma function because otherwise the numbers get so large you can't store them anymore.

[@ciaranmcevoy9875]

Great insight, I love it! Thanks pal.

[@nsuarez]

Wonderful job. Thank you! I will share with my students.

[@BladesAcademy]

I would die for such a humorous and intelligent lad in my life.

[@jan-willemreens9010]

... A good day to you Ciaran, What I can't get out of my brain about logs is: the log of a given number (argument) is that exponent by which one has to raise the base of the log to get the given number back; in short, the outcome of a log is an exponent! I always use as the example the very practical Richter Scale ( large earthquake energies represented by simple numbers ). But just to be on the safe side, I regularly briefly repeat the theory about logs, in order to be able to continue to manipulate them efficiently (lol). Your presentation increases admiration and respect for this indispensable math topic! Thank you very much for your interesting math efforts ... Jan-W

[@ciaranmcevoy9875]

Hey Jan, thanks for the lovely comment. I personally believe logarithms get lost, just as you've pointed out, from their purpose (mainly due to their name I'd say). It's forgotten that they go hand in hand with exponents. They allow you to move your mathematical efforts into the exponent space of numbers.

[@jameskirk9996]

I love the history behind logs, fascinating!

[@redhood7105]

I REALLY enjoyed the video! Great work

[@ciaranmcevoy9875]

Thanks pal!

[@aryankulkarni949]

Amazing video to build intuition and satisfy curiosity.

[@mountainman9145]

Every log video on youtube just adds to my limited understanding. This was excellent.

[@anishsharma6702]

Thanks , for explaining the work of such great mathematicians , who have shaped today our generations with their work , in an enjoyable way, hope your efforts get recognized and cheers.🎉🎉

[@ciaranmcevoy9875]

Thanks Anish! It's much appreciated, I'm glad you enjoyed it!

[@ronaldjorgensen6839]

thanks for your persistence

[@captnoplan3926]

This is great. It didn't fully click when watching other videos. I understood how it works, but I didn't understand why was it created in the first place and its application.

[@alexBaldman]

This is great and I appreciate you sir! Well put!

[@ciaranmcevoy9875]

Thanks Alex. Glad you enjoyed the video.

[@EleanorWilliams-t6f]

This was so helpful in conceptualising a concept which has been challenging to grasp. Thank you!

[@ciaranmcevoy9875]

That's so good to hear!!

[@ClearOutSamskaras]

Applications are what is so fascinating and practical: Can you do a video on the logarithmic relationship between additional units of tnt and the explosion (energy release) that results when detonation takes place?

[@ddichny]

Minor correction: Napier's name is misspelled at 1:44

[@phxm7853]

I am little late to come to know about this channel. Thank you for explaining this.

[@ubuntubantu2404]

Asante sana. Imenisaidia kujua nini hesabu hizi zinamaanisha. Kitu ambacho sikuweza kuelewa wakati nasoma mada hii nikiwa mwanafunzi wa kidato cha pili

[@ciaranmcevoy9875]

That's great to hear!

[@jewell__]

I enjoyed watching this video. Very fun and enlightening! Cheers!

[@ciaranmcevoy9875]

That's lovely to hear Jewell!

[@boggypeak9468]

Thank you. I appreciate the time you took to explain this and the beauty of the history.

[@olayinkajosiahajayi8330]

What a fantastic video! I enjoyed watching it.

[@ciaranmcevoy9875]

Thanks Olayinka, what a great compliment!

[@benjieman1821]

Thank you for that great approach of teaching the Logarithmen and thank you for leaving out to many confusing equations ❤

[@bl5240]

Thanks for this good video you deserve a bigger audience

[@tasneemtarannum5039]

While I still can't say that I truly understand the application of logs, this video cleared up much and I can honestly say I like logs a lot better than I have before. Thank you.

[@gsiehljsoeheo7652]

This video was fun and Intresting ! Loved his sense of humor.😆

[@ciaranmcevoy9875]

Thank you. That's lovely to hear.

[@MrRyanroberson1]

one more feature you didn't mention is floating point numbers in computers - these numbers are stored in binary scientific notation, which is about 80% of the way to a logarithm, and forms the basis of most of our critical multiplication operations

[@ciaranmcevoy9875]

Love this! Great addition!

[@davidcastle7212]

They are for multiplying & dividing really big or small #s.

[@jessstuart7495]

Now we need a video on the w Lambert function!

[@tarekberouijel4415]

that was a really good video, helped me find out the history of logarithms

[@ciaranmcevoy9875]

Glad it delivered Tarek :)

[@Native_love]

Great video! Thank you!

[@shravan7623]

We definitely appreciate the effort Your Excellency. Please keep them coming.

[@ciaranmcevoy9875]

Thanks Shravan, I definitely will do.

[@johncrwarner]

Being born in 1962 and was introduced to logs before I had an electronic calculator though a friend at school did have a mechanical calculator! so for me logs were a useful aid even if I did drop them as soon as in the sixth form my father bought me a calculator (with a square root function!) I possibly had a bigger problem understanding why I had to learn how to use a slide rule logs seemed so much more useful and had better accuracy but my father, who was an engineer, swore by the slide rule.

[@ciaranmcevoy9875]

Thanks for sharing this John. Yeah, once you had the calculator, I can imagine the accuracy of the slide becoming almost redundant.

[@johncrwarner]

@@ciaranmcevoy9875 I only ditched the log book when I got a calculator with log ln, e^x and 10^x buttons It was an electronic log book that fitted in my pocket. BTW I did all my mathematics exams with a ban on calculators. Though the mathematics at university was much more problem-solving than calculation.

[@ciaranmcevoy9875]

Yeah, the use of logarithms to problem solve is where they really shine and calculation only comes in to get the final value (if required). I love the notion of having an electronic log book, I know modern calculators are essentially that and more, but just the simplicity of the progression from paper to digital is rather quaint.

[@johncrwarner]

@@ciaranmcevoy9875 If you are brought up with log books with look up tables for log, ln, 10^x and e^x as well as the trig and hyperbolic functions Both the teachers and students use the methodologies of the older method like the first quantum theories versus quantum mechanics.

[@squeekycheese]

How long do you think it took after all these calculations were complete to set up the printer in the 16th century?

[@zorski1788]

Well, this is a diamond in the rough, thank you. Helped me to understand logarithms when I know where they come from

[@ciaranmcevoy9875]

This is great to hear Zorski. Glad the video helped.

[@malashukla9292]

Yes ,really enjoyed it

[@pavelperina7629]

Awesome introduction. When I tried to reinvent how and why logaritmic rule (it's slide rule in english actually) works, I came to exactly the same image as shown at 6:11. However I sort of wonder how people invented powers of weird numbers, such as 10^0.30103=2 or 2^3.3219 which is 2^(10/30103). I guess there is some method such converting log_b(x) to ln(x)/ln(b) and then using sum of some series and afaik nice square roots are done by repetition of trial-error-qualified correction based on derivation.

[@chrisdjernaes9658]

Thanks for demystifying the Math and making it fun. Cheers 🍻

[@sajademad117]

Really great video!

[@DN-sl9qb]

For say log_base10 (x), I ask myself “How many times do I have to multiply the base number by itself to get x?” And that number would give me my answer. But that still doesn’t help with understanding how to think about logs intuitively and what problems they are capable of solving and why/how they solve the problems.

[@skeleton_craftGaming]

Log is used nearly everywhere in number theory as, due to be very nature of how base systems work. The number of digits a number has is very very intrinsically tied to its logarithm in that case.

[@krishnateja7728]

I did enjoyed, amazing!

[@leslieblake9]

I absolutely loved this!

[@josephfdunphymba3241]

I lole yhat you gave burghi due credit...the meeting of napier and briggs is a classic demonstration of the scientific method at work, in spirit and indeed

[@thinkoutsidebox1276]

respect to napier, burgie and respect to you as you explained logarithm so that I can understand. Your student should be lucky. Teaching has to be like this

[@ciaranmcevoy9875]

I appreciate that, thanks!

[@adastra123]

Thanks 👏 the humour works too btw. Enjoyed the history and the problems. Subscribed too.

[@ciaranmcevoy9875]

Thanks pal that's lovely to hear

[@jakkelway]

Outstanding! Thanks mate! :)

[@ciaranmcevoy9875]

You're welcome pal

[@peterfarmer7642]

LETS GOOOO BIG DADDY CIARAN

[@AhirZamanSairi]

12:00 not true, day lengths fluctuate (increase or decrease) as the proximity of the earth relative to the sun and the moon fluctuates, but increase by about a net of 1.7 seconds each century as they both get farther

[@marciorjusto]

Hi! Excelent explanations, but what is the difference between power and exponentiation? Why in Calculus classes, teachers use only the term "exponentiation"?

[@ciaranmcevoy9875]

Great question. I differentiate between the two in my class by teaching that the power is the resulting number, i.e powers of two are 2, 4, 8 etc. Similarly square numbers are the likes of 4 and 9 etc. However, the exponent is the number of times the base is multiplied by itself.

[@godofgodseyes]

Hi Ciaran, is there a philosophy why and how Imaginary numbers exist? How do you show imaginay number representations, physically?

[@ciaranmcevoy9875]

It's a good question, when imaginary numbers were first discovered they were suggested to be called "lateral" numbers. Because they can be seen to be another dimension to our 1 dimensional number line. In essence, they're not imaginary at all. Might be worth another video :)

[@godofgodseyes]

@@ciaranmcevoy9875 Thank you.

[@GottfriedLeibniz5]

I'm neither smart nor intelligent. I'm not even good at solving mathematical problems, either. But, Every part of Mathematics is my favorite. I just love mysteries of Mathematics. Mad Respect To John Napier For Inventing Logarithms.

[@platinumphonesandcomputers]

so logarithm books where kind of multiplication calculators of those days right?

[@naikkelas7495]

you help me fell asleep, I used to visit an alcoholic anonymous group and join a street fight club but finally I found this channel, thaaanks

[@omarabdullah1197]

Definitely I do appreciate your effort. I have read and listened to a lot of resources about history of logarithms, but still l got some new information from your video. So please keep up with your great effort. I hope your channel subscribes Skye rocketing

[@ciaranmcevoy9875]

Thanks for the kind words and good wishes Omar!

[@givenfirstnamefamilyfirstn3935]

In school we used log and antilog tables without ever being made aware of the principle behind them. Perhaps it was but we (or maybe I) were/was too young and naturally ignorant to grasp the harder part, this essential cleverness from back hundreds of years earlier. I like mathematics much more many, many decades later having re-learned much of it out of residual curiosity. With a better insight I could have loved it way back then instead of just enduring the robotic procedures like grinding through some hated language. Just entering the teenage years of course carried the handicap of emerging laziness and arrogance, the best years and the worst for learning?

[@debsankarray]

Great one !

[@mohamedbelebardi1836]

Wouldn't the number of points corresponding to 20 points be 20+ (20x10) ?

[@aporifera]

Because you need another inverse for exponentiation since it's not "symmetrical" anymore when you get to this tier

[@JonJon-rj6xo]

website not available?

[@reynoldpetersen3280]

Very I interesting video. Love the history of logarithm

[@ciaranmcevoy9875]

Thanks Reynold!

[@Chekuthan0101]

Great work❤

[@aaravchandra3063]

Napier and Jost used a very tedious method, but what about Briggs. I've been beating my head over it for 2 days now and I still don't understand how Briggs calculated the value of logs, how did he make those large tables? Can you plz explain that too !!!!!

[@ciaranmcevoy9875]

Hey Aarav! I completely understand your frustration, I had the same thoughts when researching the topic. So, from my research, I found that Briggs did it two ways: One way was to calculate roots from log10(10) = 1, for example 10^(1/2) = 3.16227766 therefore log10(3.16227766) = 0.5 and so on. This makes sense and all, but does feel like starting from scratch and a lot of rework. The other way was to convert the logarithms of base "slightly greater than one", say 1.0000000001, into base 10. For instance log1.0000000001(10) = 23,025,850,929. And so to make log10(10) = 1 we can show that as equalling log1.0000000001(10) * log10(1.0000000001) (this matches up with the "change of base" formula for logarithms). In other words Brigg's needed to multiply every logarithm table entry by log10(1.0000000001) or 1/23,025,850,929 to convert it into log base 10. It's hard to say whether Brigg's converted Napier's tables, used Burgi's or created new ones, since one aspect he wanted to improve with Napier's logarithms was to use a number greater than one rather than less than one. Regardless, the premise remains the same. I hope this helps and that it makes sense. For further reading, I found this information in the books "A History of Mathematics" and "Seventeen Equations that Changed the World".

[@aaravchandra3063]

@@ciaranmcevoy9875 Thanks for both the explanation and the book suggestions, really helped. Great vid !!

[@proof6930]

I think he kept taking square root of a numerous, say 10. Eventually after taking n square roots he would arrive at the number 1 + 2.3026/2^n. This number^ (2^n) is 10, and 2.3026 is ln of 10. Now do the same for 2. This gave him 0.6931. To get the ln of 5, ln 10 - ln 2 = ln 5. So now he can get the ln of any number that is a multiple of 2 or 5. Do the same for all prime numbers. He did do some other methods for a few numbers, but that was how he got most of the numbers.

[@drivetrainerYT]

Simply joining the thanks. Very clearly put. Please carry on

[@ciaranmcevoy9875]

Cheers pal! I definitely will carry on.

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[@kf5hcr176]

You have honored your predecessors. Well done Sir.

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