What is a Natural Log Ln(x)? - Part 1 (Logarithm w/ Base e - Euler's number)
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- Опубліковано 6 кві 2020
- More Lessons: www.MathAndScience.com
Twitter: / jasongibsonmath
In this lesson, you will learn what a natural logarithm is and how it is a special logarithm. The natural logarithm is a log with the base that is Euler's number. Because the Ln(x) function has a very special base, it comes up in all branches of science, mathematics and engineering. The natural log has uses in the study of exponential systems, wave systems, differential equations, oscillating systems, quantum mechanics, and more.
Reading from comments below, I can easily say most of us still got the urge and curiosity to learn how this math actually works, no matter how long you left from school. Unfortunately majority of us just didn’t had a chance to meet tutor, not just only good at math, but also good at explaining. The urge to understand still deep inside my heart no matter how many years had past.Finally!
I relax when I watch your videos cuz I know that everything difficult will be explained fully. Thanks a lot for your massive efforts
What a nice comment! Thank you so much!
al
Jason is the best, crystal clean voice and precise explanation. Engaging, interesting and natural.
You are the greatest maths teacher i have ever had before
You are the greatest teacher of math I have ever had
Best concise description of e I've seen
You are an amazing teacher. I finished college many many moons (35 years) ago but I watch your videos to learn things that were not clear in class at that time. It’s not ‘work’ watching your videos; they are informative and a joy to watch. Thanks 🙏
my teacher looks at us like dirt, so I appreciate this, I don't feel like a dumbass watching your videos T^T
Yep. Exactly. (Teacher has been teaching for decades). Taking Pre-calculus in the summer. Therefore, these videos are invaluable.
Best video on natural logs I’ve ever seen.
Best tutor on UA-cam. Many thanks
Thank you. You can almost tell you're passionate about this. You teach it so so well. Thank you.
Jason be helping future engineers, I love his videos and he has helped me so much!
Wonderfully clear presentation!
Wow! Amazing professor 😁 thank you! I made it all the way to calc 2 with absolutely no understanding of logarithmic functions and the number e. This made my understanding crystal clear! Subscribed
You have a gift and we are fortunate to benefit from it. Thank you for sharing your knowledge!!
Great job! I’m 73 years old and have been struggling with “e” for 60 years. Wish I had you as my calculus teacher, unlike many math teachers you explain concepts clearly. Thank you
60 years:)))
Nah! He's joking. Nobody needs that time. He doesn't have basics or he doesn't care to understand it.😊
Excellent presentation, clear, concise and effective combination with graphics.
You make me love math! Your explanations are just so fantastic and interesting!! Bless your soul!!!
What a wonderfully detailed explanation of natural logarithm and Euler’s number! Big thanks!
Much appreciated Jason. Excellent presentation.
Love the way he explains the exponential and logarithms so easily.
Thank you for all your videos: I have learned so much in all topics of mathematics: and your videos explain everything so well: I learned lots of calculus, group factoring and the quadratic formula from your tutorials: I now know the formula automatically, and other formulas learned: Euler’s formula , difference on cubes; sum of cubes; compound interest formula: love your videos: better than my math teachers at school.
You are really good at teaching math! Thank you for making these excellent videos!
This is absolutely the best math channel I've come across so far. Would you please consider explain Galois fields (and thereabouts) to me? If there's anyone that could explain it to me, I bet it's you.
This channel seems to be a very valuable resource for understanding mathematical concepts and other subjects. I have been looking through the playlists for videos on logarithms, but in every one I watch you recommend going back to the initial explanation of this important topic. I have tried to locate that particular program, yet I have been unable to find it. Perhaps you could direct me to the specific video and/or arrange them in order of progression. Thank you.
this guy just outdid a semester of teaching from my university teachers in 30mins, auto-subscribed
Irrational numbers, especially the ones that come from Taylor series, are so fascinating to me.
All constants from converging sums just seem to pop out of nowhere, but they're incredibly useful.
Sines and cosines and logs are especially so bizarre in that they never seem to perfectly line up with the integers or radians that they create rationally.
You've just succeed to give us the perfect motivation to learn more about e and ln
Your videos are fantastic sir. I teach basic maths but maths was never my strong subject despite working in engineering all of my working life but I love maths when it is explained to me. I have had to refresh my knowledge before I started teaching but still struggle, fortunately, above the level that I need to deliver. But I’m a strong believer that you need a much deeper level of understanding than that of what you deliver to a class.
My problem was that many mathematics teachers made too many assumptions. Being a kinaesthetic learner, I need to take things to pieces before I understand something. Your videos give me the correct attention to detail to help me get to that light bulb moment
Thank you. It was insightful and useful..Again Thanks..
I appreciate your teaching.
My kids and I love your videos. Thank you
Thanks for the clear and lucid explanation . I always used to blindly take e and perform calculations. Now I understand the reason behind it.
Great job . Thanks
fantastic video! really clear. thanks
Thank you for the recap, feel so clear now on Euler's number, and Ln(x). ready for more logarithm now. Yeah~
Thank you sir .all the best
Good refresher
great class
very helpful~~ thanks~
You’re amazing 💛
Awww thanks!
This is real good thank you.
Yiu did an amazing job explaining ln and e.. thank you
Glad it was helpful!
Good clarity
That was class of a work, Sir...... Thank you very much indeed .
Welcome!
Real instructor of math I wish I had when I was a student of math.
I learned different between Log and expo🎉🎉.Thanks for your time and effort.Geat teacher l wish you to come and teach us live😢🎉
Excellent explanation
Glad it was helpful!
Love you board.
his amazing teacher!!!
All my life I wondered why the derivative of e^x was e^x .
Bingo !!
Thanks 👏👏👏👏
I love you, no kidding!! Thank you ❤️❤️❤️❤️
thanks for toturs
thanks for you are the best
THAKK YOU... SIR...!!!
very good
There is a technical glich while setting up payment methods in ur app ! I need to buy them how can i ??
amazing
I like your videos, but I do not understand how the slope of f(x) equals e^x = the y value. Can you please derive this? I don’t get it. Using calculus, the slope of say X equals three, or e^3 should be 3e^2, correct? What am I missing here?
thanks
Pi in case anyone is curious is a ratio of the diameter of any circle to the legth around the line around the circle. Pi made so much sense after I learned that.
How did you learn about it before that? Did your teacher just tell you it is 3.14 and a never-ending series of digits after that, and leave it at that? Circumference to diameter is the fundamental definition of pi, I can't believe any teacher would omit telling you that.
This video make so much sense but difficult to understand and wish to get more information.
So happy you liked it!
Jason, MathAndScience.com
Think teatcher i am from morrocco nice doing
Brilliant
Thank you!
So how do I solve this equation
3(ln5x)²+2ln5x-1=0
Help me with that
Good!
Thank you!
Kindly connect this Lambert's function w e^w swing between exponential function of complex number w multiplied by an exponential function of e to the power w.
This gives more information on inversion reversal function with the neutral y=x swing between the two.This means Lamberts functions may be reversed between the complex number and logarithmic number of e to the power w.What is the meaning of this Quantum mechanical theory of radio active decay? the area of emission increase or decrease accordingly.This means light rays diffused through becomes colored through logaithmic inversions perhaps may give a clue on Raman's scattering and diffusion of colors as a function of reflective diffusions as a function of molecular bonding.
Kibdly refer this to Nobel Laureates please.
Sankaravelayudhan Nandakumar on behalf of Hubble Telescope unit.
What about the area and slope line of inverse function??
Thanks
When you get into calculus, the derivative will help you find the slope of the line, and the area will help integrate the function. Know that the derivative of e^x is e^x and the integral of e^x is e^x+C where C is a constant of integration. The inverse of e^x is ln(x), so the derivative of ln(x) is 1/x, and the integral, which you will see using integration by parts, is xln(x)-x+C.
@@justabunga1 You can prove this from the power rule, when trying to integrate 1/x dx. The power rule tells us that the integral of x^n = 1/(n+1) * x^(n+1), as long as n does not equal -1. Which, unfortunately it does equal -1, when our integrand is 1/x, because 1/x = x^(-1).
So, we take the limit of 1/(n+1) * x^(n+1), as n approaches -1, while x is treated as a constant. It turns out, that this function has a hole in it, at n=-1, and that hole converges to ln(|x|).
@@carultch that's correct. The difference between the derivatives of ln(x) and ln|x| is the domain since they both came out to be 1/x. From there, the domain for ln(x) is x>0. For ln|x|, that is going to be x≠0. The integral (indefinite) of 1/x is ln|x|+C.
@@justabunga1 I once made use of this knowledge on a biology exam, where I needed to evaluate logarithms to solve a problem concerning exponential growth, and calculators were not permitted.
I had the natural log of 2 memorized as about 0.7, and knew I could do a Riemann sum of 1/x to evaluate the natural log in the numerator. Since the question was multiple choice, I didn't need to be too accurate, but it did come in handy.
Probably not the exam author's intended solution, but it worked.
Do u have answer for this sn tn
I cant find next lessons of this topic :(
What if you have e to the -1? I'm trying to graph a value of x=e^-y and can't wrap my head around it.
Given x=e^(-y)
Rearrange, and make y the subject.
Apply natural log on both sides:
ln(x) = ln(e^(-y))
Since ln is the inverse of an exponential, ln(e^(z)) = z. This means:
ln(e^(-y)) = -y
Thus we have:
ln(x) = -y
Now negate both sides:
y = -ln(x)
Now this equation is in a form your graphing calculator can graph. It should look like the graph of ordinary ln(x), mirrored across the x-axis. It will also look like the grah of e^(x), that has been rotated 90 degrees clockwise.
Good stuff! Will help me teach population growth. But a question: in MS Excel, calculating the limit function works and approaches the limit until n = 10^11; thereafter it departs from expected and by n = 10^15 the answer exceeds 3....same in Google Sheets. Here's my formula: =(1+(1/A1))^A1 Any thoughts?
This started a long conversation with some computer science friends. They attribute it to a round-off error due to floating point calculations. The answer eventually converges on 1. Same in Python I'm told.
@@DeclanJMcCabe This looks just like the limit definition of e, which is e=(1 + 1/n)^n, as n approaches infinity. You can fill in the value of e in place of this formula. To get e in Excel, type =EXP(1)
@@DeclanJMcCabe I got the same issue, where after 10^12, Excel stops converging the limit to the correct answer, because of rounding errors in floating point math. This is why the infinite series method of computing e is much more reliable than the limit definition of e, since it will not diverge from the previous precision you've already established, due to floating point errors.
Is e to the -x the same as ln x?
Super👍
Natural logarithm and venturi effect are related ????
No they are not. Although you might make your nozzle's curvature match the shape of natural log.
Those dislikes comes from unnatural logarithms
👍🏻👍🏻👍🏻
I don't really understand this one, I thought this was the way logarithms and their inverses were meant to work: loge x=y then its inverse e^y= x
How come this is placed exactly the same like this? loge x=y then its inverse e^x=y
Even typing the first out in a calculator is correct
f(a)=b
a = inverse f(b)
Example
f(x)=2x
x = inverse f(2x)
But normally we use f(x)
So need to convert 2x->x
Thus x/2= inverse f(x)
Likewise f(x)=e^x
x =inverse f(e^x)
ln both side,
ln x= inverse f(x)
We use f(x)=y
It comes from you but 1 dolar a bank and it grows second yr you will get 2 dollar second when it biggins first second you calculate second minute second millisecond how .......
I have queastion
and did he say e to the power of 0 = 1 ?
I found something wrong f(x)=e^x || f(x)=ln(x) that wrong true is f(x)=e^x || x = ln(f(x))
Actually I was wondering the same thing.
But generally we consider the domain as X and co domain as y .
F(X)=y
F(X)=log(_base) X
(Base in subscript)
What u told that would mean y is domain and X Is codomain .
But generally X we assume domain
How are you sir .tuff time is ON
I'm great - how are you?
I am all rights sir ..
24:46 ...wow
Thank you!
90 degrees
To be honest , his beard is better than me at Math
natural log
pi 3.14
2.1 x 45= 90
pi=2.1
3.14 x 30 =90
Log e= ln
Isn’t it x = ln (f(x))?!
Why do I understand this stuff.
I have now a a baby girl. Its bible and this youtube for her.😊🎉❤
WHAT?????????
LOGARITHMS!
It's the word "natural" in the name that gets my mind twisted.
He forgot to define what "a slope of a line" is. With a different definition, it would not be e. So, slope of F(x)=e**x is only equal to e**x if the definition of slope is adapted to that.
Mathematics is incomprehensible to most people because the teachers take definitions for granted.
In my last year of study of econometrics, we were presented with totally different forms of mathematics. This guy needs to define his stuff far better than he does in this vid. Perhaps he did so in earlier vids, but who is going through all that just to find definitions?
Please, understand that all mathematics, any form of it, is a construct of the mind. You think of something, make up definitions and then, afterwards, start to 'find' nice relationships like the Eurler equation. But it all depends on definitions. This dependency is what pupils need to know. You see, in mathematics, there is nothing to understand, it is just all definitions and nothing else. What is called "a solution to an equation" is just a different way to write a relationship down, and what is called "solution" is nothing but an easier way to write something down so that it can be read and understood instantly. But it is nothing but definitions, nothing but.
Without compound interest put simple interest 1+(1/365+1/365+1/365.......) =1+1 =2 only Euler cheated bankers by this compound interest every day method one dollar doubles in a year ie 2 dollar is the above method without explaining this he had gone to give every day 100 percent increase and confused the world with this unending e,. But he found e,. Good for mathematics
Can you explain any terminology of mathematics according to divine of Trinity Please ? Or according to the existence of our input of our seeing ???
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