15 - What is a Logarithm (Log x) Function? (Calculate Logs, Applications, Log Bases)
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- Опубликовано: 26 авг 2024
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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.
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…
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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.
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They use the jargons, to show how smart they are, rather than make sure that student gets education. Great job.
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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.
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He has cultivated his talents through hard work and dedication, no magic necessary.
if you used to be my teacher when I was young I would certainly have graduated, nice job
You would have certainly passed math.
English, I'm not so sure about.
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.
Wonderful explanation. Logarithm is now demystified for me. Love to see more like this. You are a GREAT teacher. God Bless you!!
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.
That is great!
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!
Awww thank you so much!
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.
A simply difficult, and easily confusable topic is so eloquently and emphatically understandable. Terrific presentation by an inspirational teacher. And he's a mathematician.
Thanks so much! I appreciate it!
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
Sir you make that so clear.You have a natural ability to make things so straight forward. You are a Gifted Teacher!
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....
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!!!
Thanks so much Sarah! Good luck in your studies and very happy you liked the lesson!
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.
Thank you so much! Good luck in your studies!
First class teaching. A great educator, and a most accomplised performer.
Was not able to understand logs before but now the concepts are crystal clear. Excellent work sir
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
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. 👨🏫
These videos helped me carry out a learning project that focuses on the application of math concepts and theories. Thanks.
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!
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
One of the best videos explanation of anything I have ever seen.
The homey Jason Gibson honestly explains logarithms better than anyone else on RUclips.
Awesome. More energy in video and easy to understand
One of the best learning channels . God bless you!
I appreciate it!
Excellent explanation. Logarithms come up all the time but trying to wrap your head around them is a rough go. Thanks for the help.
Now I understand the math of Logarithms - Log1000 x better than ever. Thank you!
That's not even an exaggeration.
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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
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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.
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.
You are a blessing, you make learning worth it. Math never seemed as interesting before. Thank you!
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
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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.
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.
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Just understood logarithmic transformation. Important in Epidemiology .Thank you very much. What a teacher!
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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.
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.
really wonderful real-life application at the end, I appreciate your efforts to teach math simplified for a ages
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.
Another great lesson, I appreciate the way you shared your knowledge. Greetings from Brasil !
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.
Wonderfully explained 🙏 God bless you for the effort , time and patience you have put into the priceless knowledge you share 🙏🙏🙏🙏 thank you Sir 🙏
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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 :)
Notice that K is on the X axis and N is on the Y axis for the exponential function; and N is on the X Axis and K is on the Y axis for the Log function. And The BASE IS NOT ON THE AXIS
YOU ARE A FABULOUS TEACHER, BECAUSE OF THIS CLASS LOGARITHM BECAME CRYSTAL CLEAR.SUCH CLASSES ARE RARE .THANK YOU VERY MUCH SIR.................
The best explanation I have found, and I've watched so many videos about logs here in RUclips.
Thanks!
I hope that someday my wealth grows exponentially so I can log your bank account with most of it because you are hands-down the greatest teacher I never had. Thank you for all of this INVALUABLE information. Truly.
Stay blessed for imparting knowledge ❤️. Very happy to relearn with utmost clarity.
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Sir, I appreciate what you are doing. It seems you did a very hardwork to prepare such video lecture.
Kind of
I am really learning maths now only. Thank you teacher. Your way of teaching is really wonderful
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Thanks for helping me understand mathematics and science in general
Happy to help
Much more useful than real classes, much more easier to understand
I'm still trying to remember the Sine of 30 degrees is one half, Cosin is rad 3 divided by 2. Why am I watching this? Because you are such a good teacher and I want to get a glimpse of What is a Logarithm. I love math and I'm soooo glad I found your channel.
Edit: The flashlight example to explain SIN and COS is guiness. You are Math, Thanks for teaching.
Hoi! Deze leraar is ZO goed man , te gek.
I finally got it stuck to my head what logs do. You got yourself a new subscriber.
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Thank you for another enormously informative video.
Heard it all before,never understood why
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I really enjoyed your lecture. You are such a great Mathematician
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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
sometimes I don't Understand How you did Something, but somehow, I Understood it after a day or after 6hrs than I talk to my brain and say where were you at that time you were absent uh? than you blame me that I didn't pay attention! anyway, the more I watch your videos the more I fall in love With Math thanks❤
One of the serious mistakes that some teachers do is that they do not explain the mathematical concepts to their students, they just assume their students know. This is a fatal mistake and leads to catastrophic results. I now keep on watching your class simply to be able to explain these concepts to my kids in simple language and I am sure they will love mathematics. Thank you sir.
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Mathematics is the orderly study of the structure and patterns of abstract entities. Pattern recognition is key. Best if you can memorize the patterns.
That how teaching should be. Thank you for this amazing lecture.
i cant believe that my professor tried to cram all of this into 20 minutes. This is lesson is amazing.
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you are my favorite teacher u made me understand every thing, :)