15 - What is a Logarithm (Log x) Function? (Calculate Logs, Applications, Log Bases)

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Math and Science

Math and Science

4 жыл бұрын

More Lessons: www.MathAndScience.com
Twitter: / jasongibsonmath
In this lesson, you will learn what a logarithm is and why they are important in all branches of math, science, and engineering. A logarithm is the inverse of the exponential function. This mean that a logarithm can reverse or "undo" the exponential operation. This makes logs very useful for solving equations that have exponential terms.
Physically, the logarithm is the reflection of the exponential curve over the 45 degree line y=x in the xy plane. We also learn the definition of the logarithm and how to convert an expression from log form into exponential form and vice versa.

Пікірлер: 481
@94233psu399154112333
@94233psu399154112333 2 жыл бұрын
I’ve been an engineer for 36 years. I struggled for a bit early on.. I wish I had a teacher like this guy, as I know I would have done better and not have had the early doubts about my chosen profession. He needs to teach teachers…
@lachuck2476
@lachuck2476 2 жыл бұрын
Amazing story.
@user-bw9zv9kf2c
@user-bw9zv9kf2c Жыл бұрын
Me 25 years of being engineer and now a teacher. But what this guys doing is beyond all my abilities of teaching
@ericmunene8521
@ericmunene8521 Жыл бұрын
Am 24yrs struggling with my mastery of digital signal processing. This guy is a miracle for me
@shetheyithe8894
@shetheyithe8894 Жыл бұрын
I am studying about it .
@Bbbbbbbbbbhhhhhhh
@Bbbbbbbbbbhhhhhhh 8 ай бұрын
I’m going for engineering too, maths and physics were not strong points for me at all, but watching videos and studying has really put me in a better place even if I feel overwhelmed. It’s because of people like this guy and also the organic chemistry tutor that I have got better at physics and maths in many ways, enough to start understanding the things I am doing more and more. Amen for these people bro.
@hermitcard4494
@hermitcard4494 3 жыл бұрын
This types of classes are even better than real time live online streaming. Being able to stop the video, rewind, replay is AMAZING and USEFUL.
@charleslowe522
@charleslowe522 2 жыл бұрын
These classes are the best, I really wish I would've had something like this at my disposal when I was in college. Especially when I took engineering physics II, because I had no notion of electrical or magnetic fields or properties.
@adammcallister9675
@adammcallister9675 Жыл бұрын
These series do an amazing job of how they explain as well. It is very polished and eliminates a lot of the need for a live person by being so clear and well presented.
@kenthaugum8671
@kenthaugum8671 10 ай бұрын
​@@charleslowe522¹¹q¹qy
@putinscat1208
@putinscat1208 9 ай бұрын
Yes, when they are good. The only advantage to live is the ability to ask questions.
@kaili1094
@kaili1094 Жыл бұрын
Have an amazingly clear vision of Logarithm now, but I have to follow you to the next class when my memory is still fresh! I can't express my appreciation for this teacher. You are amazing.
@callofduty4702
@callofduty4702 4 жыл бұрын
You are an excellent teacher. I love the practicality that you put in your lessons. This is worth gold.
@MathAndScience
@MathAndScience 4 жыл бұрын
Thanks so much David!
@gav-ce5cm
@gav-ce5cm 3 жыл бұрын
Hi david
@mathsfamily6766
@mathsfamily6766 3 жыл бұрын
You are the explainer!love your lecturing
@rajendrapatnaik9976
@rajendrapatnaik9976 3 жыл бұрын
My mathematics teacher Rout didi was also equally good like you.
@mathsfamily6766
@mathsfamily6766 3 жыл бұрын
@@rajendrapatnaik9976 great
@akmzahidulislam2764
@akmzahidulislam2764 3 жыл бұрын
I'm a 60 y/o, engineer. Relearned from you how to make the math concepts clear to the students and instill enthusiasm in the receptive minds. This class i would rate the best ever on this topic. Wish you had been my teacher 45 years ago. Love you teacher!
@farjanasharminswarna2450
@farjanasharminswarna2450 4 жыл бұрын
Thanks a lot for putting so much effort to teach us all these amazing stuff, Sir. I missed out all these details in high school and now when I am in college doing my Bachelor in Electrical engineering, I wish I could go back to that time and learn all the things that my teacher didn't taught. Now that I have a LOT of time for the COVID-19 situation, I am using this time to watch your tutorials as much as possible. This is helping me A LOT to clear my doubts. You have a gift of teaching. Wish I had teachers like you here.
@sethfrederick1336
@sethfrederick1336 2 жыл бұрын
Too heavy on the words girl dude,
@l.s.754
@l.s.754 3 жыл бұрын
Perfect. You are the greatest teacher. Reason being, you try to explain, bases, so one can understand and derive a conclusion. Most university professors teach to confuse. They use the jargons, to show how smart they are, rather than make sure that student gets education. Great job.
@rosannfitzekam5315
@rosannfitzekam5315 3 жыл бұрын
I read your bio and am amazed that a literal rocket scientist can explain things so clearly that the rest of us "normal" people can understand them. You are a great communicator and clearly care about your students. Thank you so much!
@The-BTC-Eagle
@The-BTC-Eagle 3 жыл бұрын
WOW, this absolutely stomps on any academy lessons... You explained it all without assumptions that we already know something... Absolutely great instructor!
@guymunson4863
@guymunson4863 3 жыл бұрын
Thanks for the first full explanation on logarithms that I have ever found. It's cleared up everything. You are easily the best teacher online.
@petercollins4516
@petercollins4516 Жыл бұрын
Incredebale : I am French, 80 years old and I follow your wonderful curse with passion: Because despite my bad English knoledge I found out that all yours curses are quite comprehensif and clear. I wish i coud have encounter such a Professeur when I was yung: Congretulation and great respect for such a talent of pedagogy, Peter.
@tonybatycki
@tonybatycki 5 ай бұрын
Much respect, Sir
@TheBackyardProfessor
@TheBackyardProfessor 3 жыл бұрын
I LOVE, LOVE, LOVE how you explain things so very easy and thorough. You are without question my very favorite math you tube source. You ARE appreciated! I bought all your set of DVD's years ago - like 30 of them, the algebra, trig, and calculus series. Absolutely sensational. Now I am enjoying you on you tube. You have actually gotten MORE thorough through the years! I LOVE THIS!
@MathAndScience
@MathAndScience 3 жыл бұрын
Awww thank you so much!
@whipmakingjosy1759
@whipmakingjosy1759 4 жыл бұрын
if you used to be my teacher when I was young I would certainly have graduated, nice job
@alvaropena5540
@alvaropena5540 3 жыл бұрын
You would have certainly passed math. English, I'm not so sure about.
@kimbell6689
@kimbell6689 3 жыл бұрын
This is the BEST lesson on logs I have found. You, as a teacher are VERY good at your craft! Thank you so much for making this video.
@cjoarder
@cjoarder 2 жыл бұрын
Wonderful explanation. Logarithm is now demystified for me. Love to see more like this. You are a GREAT teacher. God Bless you!!
@theholyghost
@theholyghost Жыл бұрын
The homey Jason Gibson honestly explains logarithms better than anyone else on KZfaq.
@Anonymous-gq7kj
@Anonymous-gq7kj 2 жыл бұрын
Sir you make that so clear.You have a natural ability to make things so straight forward. You are a Gifted Teacher!
@tylersteffensen9268
@tylersteffensen9268 11 ай бұрын
This video nailed it, I was looking for how logarithms are useful in practice and the Richter scale example got me that much closer to understanding.
@Max47340
@Max47340 3 жыл бұрын
Oh man, you are the best math teacher on earth, period! God has given you extraordinary talents to help humankind, thank you sir!
@isaiahperez1115
@isaiahperez1115 3 жыл бұрын
He has cultivated his talents through hard work and dedication, no magic necessary.
@DikchyantAdhikari
@DikchyantAdhikari 3 жыл бұрын
You are a blessing, you make learning worth it. Math never seemed as interesting before. Thank you!
@TheLazyLarryShow
@TheLazyLarryShow Жыл бұрын
First class teaching. A great educator, and a most accomplised performer.
@chemanywhere4659
@chemanywhere4659 4 жыл бұрын
Can't miss a thing when listening to the explanation. it's so full of information and no short or long cuts taken. Thank you for sharing to us clearly your own understanding of logarithms.
@MathAndScience
@MathAndScience 4 жыл бұрын
Thank you so much! Good luck in your studies!
@tadasvaznevicius4829
@tadasvaznevicius4829 3 жыл бұрын
I am from Lithuania , I have seen many of you videos and there is one thing to say ,anything you explain is very easy to undesrtand. Thanks a lot for effort you put in to explanation. Many teachers should take lesson from you . Awesome!
@JohnLincolnUSA
@JohnLincolnUSA 2 жыл бұрын
You are a superb teacher….why weren’t there teachers like this when I was having my early education!
@achseasonsinvestment5474
@achseasonsinvestment5474 3 жыл бұрын
You deserve your title as a teacher thanks so much you have helped me understand a lot of stuff that my own teacher was failing to teach me now im certain that im going to pass my exams all i need is to follow your videos.
@MathAndScience
@MathAndScience 3 жыл бұрын
That is great!
@beaubuffington
@beaubuffington 3 жыл бұрын
You are truly an amazing teacher! You teach with confidence, and that inspires confidence! Thank you! Finishing a civil engineering degree after 30 years with your assistance....
@shahjaani5166
@shahjaani5166 3 жыл бұрын
Thank you so much for doing this mathclass. Never had a teacher who can explain these things the way you do..not even on my College courses have I had one. Thank you once again we appreciate it.
@preetisharma-kj8nh
@preetisharma-kj8nh 3 жыл бұрын
Was not able to understand logs before but now the concepts are crystal clear. Excellent work sir
@kimberlydavis7322
@kimberlydavis7322 2 жыл бұрын
Thank you so much for actually explaining these math functions...it really helps to retain information when you understand how and why they're applied
@beethovensg
@beethovensg 4 жыл бұрын
A simply difficult, and easily confusable topic is so eloquently and emphatically understandable. Terrific presentation by an inspirational teacher. And he's a mathematician.
@MathAndScience
@MathAndScience 4 жыл бұрын
Thanks so much! I appreciate it!
@isaiahperez1115
@isaiahperez1115 3 жыл бұрын
You've set the standard for teaching. All teachers could learn from your methods.
@olydnk5270
@olydnk5270 3 жыл бұрын
Just understood logarithmic transformation. Important in Epidemiology .Thank you very much. What a teacher!
@dimidomo7946
@dimidomo7946 2 жыл бұрын
First-rate teaching lesson. Thanks Math and Science for the lucid and enjoyable introductory entrée into understanding logarithms. I didn't even feel the need to take a bathroom break.
@rizanz2108
@rizanz2108 Жыл бұрын
These videos helped me carry out a learning project that focuses on the application of math concepts and theories. Thanks.
@vascobishop6834
@vascobishop6834 3 жыл бұрын
Effort, Effort and more effort from someone who wants to educate and share the secrets of maths with the world. A magician with maths on a mission to make us all to become aware of some of the mysteries of this planet.
@ranierymonteiro4135
@ranierymonteiro4135 3 жыл бұрын
Another great lesson, I appreciate the way you shared your knowledge. Greetings from Brasil !
@sarahohara3125
@sarahohara3125 3 жыл бұрын
I almost never comment on videos, but I have to thank you - sincerely, and from the bottom of my heart - for this series of videos. I'm in my second semester of college chemistry, and all of the sudden we are seeing equations with Log and ln and e and I had no idea what they were. There was no support in the chem book because they assume you know them already. I watched four or five videos today before I got to yours, and this is by far the best, most thorough, most understandable way I have seen it explained.Thank you so much!!!
@MathAndScience
@MathAndScience 3 жыл бұрын
Thanks so much Sarah! Good luck in your studies and very happy you liked the lesson!
@marvinscruggs4742
@marvinscruggs4742 7 ай бұрын
He always goes the extra mile to make you understand what he is teaching. Splendid!
@fernandobailey4572
@fernandobailey4572 2 ай бұрын
One of the best videos explanation of anything I have ever seen.
@wellyenas994
@wellyenas994 9 ай бұрын
Thank you so much. You are one of the best teachers around. I am pointing all my kids who are taking science and economics to your channel. Much respect and appreciation.
@rezahasan25
@rezahasan25 4 жыл бұрын
One of the best learning channels . God bless you!
@MathAndScience
@MathAndScience 4 жыл бұрын
I appreciate it!
@Songfugel
@Songfugel 2 жыл бұрын
This was so well approached, and the opening explanation was exactly the reason I've had problems for the past 30 years as an engineer every time I have to use logarithms. I always knew how to use them, but never truly understood them until I absolutely had to when I jumped into machine learning and data engineering. ps. anyone else noticed how all mathematical & engineering men seem to gravitate to this exact same handwriting? It is the exact same as mine, and in almost all videos I've seen recently, they use the exact same style and look, even down to small quirks in it. However, female engineers and both men and women in other fields, tend to have quite different, way more flowy handwriting, even when using the same handwriting style
@martinvanhasselrolle2509
@martinvanhasselrolle2509 3 жыл бұрын
You are helping us to understand that science is available for all who really love it and are determined to learn it and not only for the cleverest and most extraordinary minds. With work, passion and a great teacher we all can make it! Many thanks!
@jmcuzzupe84
@jmcuzzupe84 2 жыл бұрын
You’re a great teacher … thanks for your tutoring … I’ve been taking online courses towards my degree in mechanical engineering, and you know, every little bit helps.
@22niloc
@22niloc 8 ай бұрын
Very grateful to you for putting this out. I'm beginning a new career in data analysis and you've helped me take a whole step forward in a 45 minute lesson.
@cresmalynejoyr.demesa4639
@cresmalynejoyr.demesa4639 7 ай бұрын
I've been struggling in math, literally. Thanks to you for all your clear and understandable teaching techniques.
@frankmccann29
@frankmccann29 3 жыл бұрын
You remind me of the professor who fina)y enlightened me on Laws of Math. Got a B and was happy. You have the rare ability to break Math down so others can love it. Thanks again
@marklouiston2442
@marklouiston2442 Жыл бұрын
Thank you very much for explaining math concepts so well. You have a great way of putting concepts into understandable language.
@bandaradiss8092
@bandaradiss8092 2 жыл бұрын
simply i couldn’t stop listening to this excellent math teacher. cheers,
@constantineeleftheriades3819
@constantineeleftheriades3819 2 жыл бұрын
Thank you so much for making this. I came across logs while researching to learn more about chemistry, so and I was very curious about how it worked. This video is excellent, you are very good at explaining things :)
@ponzianomanning3071
@ponzianomanning3071 3 жыл бұрын
Now I understand the math of Logarithms - Log1000 x better than ever. Thank you!
@simpleman283
@simpleman283 2 жыл бұрын
That's not even an exaggeration.
@elismantovani3638
@elismantovani3638 4 жыл бұрын
I loved your lesson! You explained it very well and bring also so many plus informations! It was excellent!
@mariocesarsousa
@mariocesarsousa 3 жыл бұрын
I remember how strange it was this funtion. It seemed useless and strange. Your explanation clears out my mind and proves its importance. The digits representation , the number of zeros, were never taught when i was at school. The Richter scale explanation was awesome. To know what the graphs are about when earthquakes appear as TV news or science news is really interesting, and the most important of all is that you help people understand it. And That's what you are doing in such a clear and motivated way. Thank you very much for giving the best in your teaching. 👨‍🏫
@glennricky
@glennricky 2 жыл бұрын
Stay blessed for imparting knowledge ❤️. Very happy to relearn with utmost clarity.
@nelibethluna-zm7ft
@nelibethluna-zm7ft 9 ай бұрын
Thank you so much, Sir. Your explanations are truly helpful. Wish the hidden videos wont be hidden anymore. Anyway, I am still truly grateful. God bless you for generously and patiently making these worthwhile and very helpful videos.
@leahpeya9106
@leahpeya9106 2 жыл бұрын
The best explanation I have found, and I've watched so many videos about logs here in KZfaq.
@MathAndScience
@MathAndScience 2 жыл бұрын
Thanks!
@josephkingston9252
@josephkingston9252 Жыл бұрын
I have met a number of people in my life that were good at their trade or occupation or their calling in academics or vocational field but even though they were wonderful and Highly skilled, they did not have the talent to teach it to others they were either impatient or just did not know how to explain it well. I wish I would have had this guy for my math teacher , in the 10th grade I even went to the principal and turned in my math teacher and reported him as being one that couldn't explain algebra good enough to understand it, of course they took the teacher's side , but you know you really don't know how much you really missed out on until you see a guy like this guy, he is personable, intelligent and he knows how to explain it. I have found that in math, if you ever purchase a math book and after the person's name if it has PhD forget it do not purchase that book usually those books you cannot understand anything they're teaching in it , I'll give you a good example in the field of pipe fitting you have to know right angle trigonometry to do offsets, and the best teacher that I've ever come across was Johnny Hamilton who was a pipefitter himself and he taught trigonometry in the book that ended up selling in Walmart stores in such a simple way to where people in the pipe field could understand it, if you would have attended a local college you never could have understood it the way he taught it , oh yes , if I would have had this guy as my teacher I probably would have chosen math as my favorite subject and he's right I've had college chemistry before and you have to know logarithms or you cannot keep up with college chemistry
@dbharathi2003
@dbharathi2003 Жыл бұрын
Awesome. More energy in video and easy to understand
@user-pl2kd9vm8z
@user-pl2kd9vm8z 5 ай бұрын
This was extremely helpful ! Thank you so much for making these concepts so practical and easy to grasp . You are brilliant and much appreciated ! 😊
@RD2564
@RD2564 2 жыл бұрын
Thinking of the inverse function as being the function that undoes the action of the original function is a nice way to look at it and I never thought of it QUITE like that for some strange reason ... thanks!
@everistobwalya551
@everistobwalya551 3 жыл бұрын
I really enjoyed your lecture. You are such a great Mathematician
@lennardcaydenlee5456
@lennardcaydenlee5456 9 ай бұрын
really wonderful real-life application at the end, I appreciate your efforts to teach math simplified for a ages
@Imustfly
@Imustfly 3 жыл бұрын
A logarithm is simply an exponent used to describe all the numbers that fall in between the whole number exponents (2,3,4,5,6,7 etc) powers of 10. Ex. The number 180 can be described as 10 raised to the 2.2552725021 power, whereas 500 is 10 raised to the 2.69897000434 power. I remember teaching logs in the USAF as a recon tech/instructor for students in the photographic science career field. We taught the short cut that for a POSITIVE number, the Characteristic (whole number portion of the exponent) was a number that was ONE LESS than the number of digits immediately to the left of the decimal point. For negative numbers, the Characteristic was one more than the number of zeros immediately to the right of the decimal point. The mantissa was found in the log chart, if my memory serves me correctly. So,..for the number 12,657.00, the Characteristic is 4, since there are FIVE numbers to the left of the decimal point . For the number .000027 the Characteristic is -5 since there are four zeros to the right of the decimal point.
@davidmccaffrey4020
@davidmccaffrey4020 3 жыл бұрын
Great teacher. Really appreciated. We have a lot of good people in this world! 👌
@elainekhonggoh9335
@elainekhonggoh9335 3 жыл бұрын
Before this video, Log was just a button on the calculator. But your video changed that ! Loved your energy, and you made everything so clear.
@alialalwany9797
@alialalwany9797 4 жыл бұрын
You are amazing !!!!! Auhhhhh...I don't what to call you a teacher or scientist but it seems that you have done them all !!!! I admire your work &really appreciate it/////thnx for things U give for those who needs it (100%knowledge!!!) Watching your lectures from//////// Iraq
@emmaswepston
@emmaswepston 2 жыл бұрын
Outstanding work. SO helpful. Thank you so much.
@johnwebb2562
@johnwebb2562 4 жыл бұрын
Fabulous teacher, very rare. God's gift to humanity. Massive thanks. John.
@8DINFINITESTUDIO
@8DINFINITESTUDIO 4 жыл бұрын
YOU ARE A FABULOUS TEACHER, BECAUSE OF THIS CLASS LOGARITHM BECAME CRYSTAL CLEAR.SUCH CLASSES ARE RARE .THANK YOU VERY MUCH SIR.................
@edgepixel8467
@edgepixel8467 2 жыл бұрын
I finally got it stuck to my head what logs do. You got yourself a new subscriber.
@SixStringsAndBeyond
@SixStringsAndBeyond 3 жыл бұрын
i like your quest for understanding. thank you for the time and effort you put into making these videos. have subscribed.
@theisegeberg
@theisegeberg Жыл бұрын
Thank you for taking the time to make this video.
@navindraarjunaabeyesekera7864
@navindraarjunaabeyesekera7864 2 жыл бұрын
I have nothing to say except that you are an exceptional teacher
@maxnakhapetian1937
@maxnakhapetian1937 2 жыл бұрын
Thank you so much for these videos, they're the best! Great work
@naydenelee158
@naydenelee158 3 жыл бұрын
great videos. love your style on explaining things.
@zozawalababa428
@zozawalababa428 2 жыл бұрын
You are a great teacher.. one of the best I have ever came upon.. jason 👍👍👍
@gemmalawless7856
@gemmalawless7856 Ай бұрын
Thank you for another enormously informative video.
@jay22197
@jay22197 3 жыл бұрын
i cant believe that my professor tried to cram all of this into 20 minutes. This is lesson is amazing.
@raymondallenjhangiani7670
@raymondallenjhangiani7670 2 жыл бұрын
Wonderfully explained 🙏 God bless you for the effort , time and patience you have put into the priceless knowledge you share 🙏🙏🙏🙏 thank you Sir 🙏
@ericboakye844
@ericboakye844 Жыл бұрын
one of the best teacher I ever seen
@jhecht99
@jhecht99 4 жыл бұрын
this guy is an excellent teacher.....I want to thank him personally
@steadyeddy6526
@steadyeddy6526 4 жыл бұрын
NICE lecture, good clear explanations.
@mesfunghebreab
@mesfunghebreab 2 жыл бұрын
Much more useful than real classes, much more easier to understand
@KurdstanPlanetarium
@KurdstanPlanetarium 3 жыл бұрын
Thank you for your great lessons. very useful
@hikmatullahpakhtoon3694
@hikmatullahpakhtoon3694 3 жыл бұрын
Sir, I appreciate what you are doing. It seems you did a very hardwork to prepare such video lecture.
@destinyovbiebo8988
@destinyovbiebo8988 3 жыл бұрын
Kind of
@cellmaker1
@cellmaker1 5 ай бұрын
Excellent explanation. Logarithms come up all the time but trying to wrap your head around them is a rough go. Thanks for the help.
@gautamroychoudhury2735
@gautamroychoudhury2735 Ай бұрын
Wonderful explanation. Hats off to you.
@ayushchavan2741
@ayushchavan2741 Ай бұрын
I'm so addicted to his coloured marker pens😮😮 and my mind is 🤯 when he uses green on the graph. OMG so artistic. Jokes apart, we should actually save his intuition based teachings for the students in the post apocalyptic times in the future. ... seriously.
@Rajb90
@Rajb90 3 жыл бұрын
The best teaching method, thank you sir
@BestoftheClassofVictory
@BestoftheClassofVictory 6 ай бұрын
Nobody has ever taken the time to help me at anytime in my life This is the first time I am beginning to understand something meaningful, beautiful about the world I live in I would like to become a constitutional Law student at Broklyn Law school in New York, but I dont see it becoming real eventually I woukd like to attend The London School of Economicss, and comeback home to help the US government with their Budget Defecit issues I dont see how I could possibly pay for all this but I will take it one day at a time... Thank you for helping me, and I hope your time will not go in It will make me happy tosee my dreams come through
@dorischoo
@dorischoo 3 жыл бұрын
Excellent tutorial understanding Logarithm. Log 😱 me. After this I feel more confident thanks 🙏 Jason.
@manando1679
@manando1679 2 жыл бұрын
just brilliant. if my teacher had t(r)eached me the way you do, I would have loved math back in the days at school.
@johnbyrne6631
@johnbyrne6631 Жыл бұрын
The best maths teacher on youtube
@charlesackman6778
@charlesackman6778 2 жыл бұрын
I am 65yrs old and for the 1st time someone has explained that the base is not a counting system, but a coefficient. The u young man
@mrgeorgejetson
@mrgeorgejetson 2 жыл бұрын
Great lesson! And man... that "It's a button on your calculator" story at the beginning really speaks volumes about terrible teachers with incurious minds everywhere. Just brutal.
@is-ig4zh
@is-ig4zh 3 жыл бұрын
Man, this guy is really awesome at teaching others. Thank you so much, sir!
@corradotrasforini9563
@corradotrasforini9563 4 жыл бұрын
Great. I love your practical applications
@MathAndScience
@MathAndScience 4 жыл бұрын
Thank you so much! Jason, MathAndScience.com
@260bill260
@260bill260 3 жыл бұрын
Excellent. Thanks for being a great teacher.
@Don-kk7ou
@Don-kk7ou 5 ай бұрын
This man is a genius.. ! He is gifted to transmit the knowledge.
@irfankhan-hr1eb
@irfankhan-hr1eb 2 жыл бұрын
i have no words to appreciate this impressive hard work .👍👍
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