Logarithms: What problem was Napier trying to solve?

This is another incidental video I am using for a course on logarithms.

[@b1948j]

I've used logarithms for over 50 years and never really understood them until now. I could get the right answers but didn't understand why. It was always a struggle to memorize the rules. Thank you for explaining this so well.

[@anuvette]

How old r u coz u look less than 50

[@aymanbari974]

Explains a complicated thing in a simple fashion way, good job!

[@rodriqcc]

Thank you for clearing that enigma up for me! Understanding origins of modern mathematical devices really helps in memorization of their accompanying rules.

[@TheDitronik]

The form of multiplication was used in the 1202 Liber Abaci and 800 AD Islamic mathematics and known under the name of lattice multiplication. "Crest of the Peacock", by G.G, Joseph, suggests that Napier learned the details of this method from "Treviso Arithmetic", written in 1478.

[@gregcorcoran5847]

Wow I’ve been looking for this information for over a year. I’ve watched dozens of logarithm videos and I’ve never actually seen someone explain what it was and the insight that they are powers is so straightforward. Genius. Thank you so much.

[@alexandrianova6298]

2:18 - 2:36 is a pretty helpful way of putting it, and a video on that in its own right could be quite clarifying

[@JohnCorrUK]

What a brilliant explanation and lecture Dr James -Bravo

[@Chrls5]

it's Funny, in electronics, telecommunications, we use logarithmic amplifiers to multiply very small analog voltages very fast, WOW!

[@duckymomo7935]

Logarithms had a different use in history but we still use them today because log transformations are still useful and important for us today

[@jharwood9795]

Great video, I now understand where Napier was coming from!

[@amanettien]

Thank you. You made thing clear in less than 5mn great work

[@maverikmiller6746]

This is what I was looking for. Thanks a lot.

[@mykofreder1682]

Saw a trig story where they created tables for trig functions and there were multiplication to addition trig identities with these functions. Logs are still used for the same reason FFTs are used to cut down on the massive amounts of computing an exact value vs a good enough value. Without the tables of exponents with logs it might not be such an advantage, calculating 10 exponents, adding, then taking the exponent of the result vs multiplying 10 numbers. Doing exponent notation on computers is similar 1.234*10**44 * 2.345*10**35 can be done with float or double precision math but not 32 bit int, you lose precision since the numbers were chopped like logs. Software math processing units with open ended numbers (no bit limit) and precise values are still used in things like prime numbers or digits of Pi.

[@nathanielb3510]

The process was called prosthaphaeresis, and existed a couple decades before the existence of logarithms.

[@ingiford175]

And it was mostly used on ships for determining positions. A sextant, a book of log tables, and some addition in your head, and you can help find your position by the stars.

[@mgmartin51]

One of my favorite books is by Eli Maor called “e: the Story of a Number “ where he recounts the origins of e and logarithms.

[@keithwalker6892]

I gave this definition of what a logarithm was to my lecturer at Caulfield Technical College Melbourne Australia in about 1944 .The Logarithm of a number is the power to which the base must be raised to equal number .So base ten must be raised to power 2 to equal given number 100, so log of 100 to base 10 is 2

[@jogeshjoshi2535]

Many many Thanks

[@suevanhattum]

I had no idea that the math folks didn't know at first that logs are powers!!! (Is there something readable on this?)

[@josephmalone253]

Good old Kames he was probably using Greek methods and thinking of zeros paradox. Greeks viewed all math as ratios of line segments or divisions of a square. They didn't have Arabic numerals so the made much use of geometry.

[@christinekincaiddewey4791]

As I would tell my sophomore students, the key to understanding logarithms is to keep repeating the phrase “logs are exponents”!

[@miszcz310]

Small comment the numbers you wrote are not Napier's logs these are 'common' logs or logs with base 10. They came later (just by changing the base of Napier's natural logs)

[@globalcitizen995]

Excellent point. I must have been half asleep not to notice that, though I suspect it is a case of what might be called a 'trick of the mind' where one goes down a certain road from a particular starting point and everything is logical and so the brain doesnt question it.

[@someonespadre]

I have cracked open 2 books, Dr. Bruhns logarithm tables and a book of logarithmic sines, tangents, cotangents and cosines probably for the first time in decades.

[@davidwilkie9551]

Or observed e-Pi-i sync-duration connectivity is AM-FM Communication in superimposed alignments, and real-time instant i-reflection tangency of the roots 1-0-infinity, instantaneous conic-cyclonic Entanglement occurs in real number multiples of probability as log-antilog => orthogonal-normal picture plane Condensates.., which is another more complete version of the fixed Interval vs the parallel coexisting logarithmic ratio-rates as shown. Reciproction-recirculation at phase-locked e-Pi-i coherence-cohesion instantaneous sync-duration has the inherent "cooling curve" Inflation-condensation modulation cause-effect of Perspective Projection Drawing Conception. So the idea is built into us as Condensates of log-antilog time-timing sync-duration, simple in operation but very complex to analyse and develop a system you can quantify to describe in FormFunction.

[@kubatuggat8087]

2:13 "I do not know" gives hope to student because student think teacher know every single things (which is not true every time).

[@Labs51Research]

This was brilliant ... this is how things should be explained~!

[@allfires4957]

Beautiful

[@alittax]

Beautiful, thank you!

[@joro8604]

Enlightening

[@endo9902]

very nice video.. bringing the math to the human level..

[@beutyindetail]

4:25 just wow😊

[@robertwalker-smith2739]

I actually understand the topic less now than before I watched this.

[@jairusenad9333]

Robert Walker-Smith that’s learning

[@texasdrz9515]

Lol that’s my daily experience when learning.

[@areebhussain321]

great stuff

[@walterisraelmoscosozarate8768]

You Explaine The Napiers Plates my friend

[@bmzaron713]

Awesome video but wouldn't it be named inverse exponentials or something related? Maybe I'm way off but I usually think of 'powers' when dealing with roots and the inverse of that which are powers (squared, cubed, etc..) .. Logarithms and exponents go hand and hand much like addition undoes subtraction and division undoes multiplication and roots undo powers... Now I'm talking to myself.. It's just kind of funny how logarithms solve for exponents but exponential functions you plug a value into the exponent.. I feel like powers/ exponents describes them both best, but then again they are inverses so it's all related, circle of life

[@lastyhopper2792]

Does this man write mirroredly and with left hand??? That's insane if that's true.

[@eeltauy]

Great channel

[@melindabrown2955]

He has been a very long time to me today and that’s bad cause I need to do other stuff

[@sharonjuniorchess]

Its simple. Convert all your numbers to binary then all the arithmetic is about adding or subtracting.

[@saranzaibkhan890]

thank u for explaining the log of base 10.. can u plz explain where this e came from in log.. and made it natural log.?

[@yanceytemple9572]

kzbin.info/www/bejne/fHOWkHWbqtB1eM0 I just watched the above video and he explained it. I have to teach Log's for the first time in my 20 year career as a teacher this up coming year and I am going to be relying on these guys for some explanations I can use with my algebra 2 classes. Very helpful videos.

[@someonespadre]

e (2.7183) is related to a limit on growth, compounding interest on a bank account increases annual yield if it is compounded more often but e is a limit that it never quite reaches as interested is compounded more and more often. It is used as a base for so-called natural logarithms.

[@lalune9938]

How did he do it? I mean, the words and numbers were supposed to be seen backwards! He stood behind the glass so he couldn't write backwards like that?????

[@cristianreyes8288]

Millah Harris they just reflected the video

[@someonespadre]

He filmed it then they mirrored the video. Notice his shirt is overlapping the wrong way.

[@freefreeman6873]

No the question is how did he make the tables

[@alibaliindah8199]

I don't get it, 2 to the exponent 3 is 8, 3 to the exponent 2 is 9, 2 X 3 Is 6, anyone can explain " log is just exponent backwards"?

[@sharonjuniorchess]

2x2x2 = 2³ = 8. So 2^x = N and x = Log₂(N). To work backwards if you know the result is 8 how many times do you have to multiply your base (in this case 2)? Log ₂ (8) = ?? the answer is 3. www.mathsisfun.com/algebra/logarithms.html N.B. If you don't have a function on your calculator to enter base use: Log 8 ÷ Log 2 = 3 If you are working with a base of 2 then you can see the relationship between the exponent (on y axis) and the product N (on the x axis) in this graph. en.wikipedia.org/wiki/Binary_logarithm

[@petergore1972]

Peter Gore Seer, John Napier Was A Warlock, Delving Into Paranormal,And Practicing The Art Of Witchery,And A Christian With His Hand On The Bible.

[@melindabrown2955]

I don’t know what long division

[@melindabrown2955]

Is

[@melindabrown2955]

He has been a very long time with my day t

[@melindabrown2955]

What’s a log

[@thomasolson7447]

a grumpy

[@jonathanharoun5247]

So why did euler's number show up in one of his log tables (in the form of natural logarithms)?

[@ahmadawalluddin8711]

what the answer to your last question? did you meant for provocations?

[@CE113378]

The logarithm is the exponent. The exponent itself is not the power. For example, when you see 2^3 = 8, 8 is the 3rd power of 2. 8 is the power; 3 is the exponent. So, when we say "2 raised to the 3rd power," what we are really saying is that the end of result of the operation lands us at the 3rd power of 2; that is, 8. But 3 is the exponent. 8 is the 3rd power of 2.

[@tasninnewaz6790]

Sir, please upload more videos about calculus.

[@geraldillo]

Great explanation!

[@glorywisebeat3032]

I am relly confused about this logarithm have been trying it a lot

[@hamzamohamed7935]

Wow

[@kamrunnesa5769]

wait,then how did napier found logs?

[@nightmare9597]

He multiplied everything for 20 years

[@dara_1989]

in india .. schools give log table book instead of a calculator 🙄 ... which obviously no one uses 😂

[@qzorn4440]

some very interesting information from a different view. thanks. 8*7)

[@ufcfightfansmizo6260]

Thank you so much, but If you say why should we care then why do you explain😂😂😂😂

[@sebastianbalbo1906]

Jaina mathematicians came first..

[@tonymartin5004]

Helpful

[@HailAnts]

Calling them ‘powers’ doesn’t really help much. How does an average person raise a number to a fractional decimal? What is 10 ^ 0.688?!

[@alvarogoenaga3965]

I always wonder about the same. It happens to be that integers, and to some extent rational numbers, work as "powers" in the exponential function. This particular function originated from the need to facilitate calculations and from the properties of geometric and arithmetic progressions. Anything in mathematics , no matter how complicated, goes back to simple arithmetic.

[@christopherellis2663]

There are better ways to do multiplication ✖️

[@acajutla]

But this is multication

[@gauravraj4507]

Lazy person always make things simpler..

[@timokimo8206]

Logarithm was invented by muslim called "Al-khawarzmi"

[@benquinney2]

Slip stick