Logarithm Fundamentals | Ep. 6 Lockdown live math
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- čas přidán 4. 05. 2020
- Back to the basics with logarithms.
Full playlist: • Lockdown math
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• Triangle of Power
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Hebrew: Omer Tuchfeld
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Grant: “this series is directed towards high school students”
Also Grant: “if you have a child around the age of 5...”
If you have *access* to a child... so both siblings and random children you grab off the street both count too...
@@SimonBuchanNz Is there not a lockdown in your country? Or are children to you like are unit circles to Grant.
@@holctomaz2562 New Zealand, we went from level 4 ("essential" business only) to level 3 ("safe" - eg you can merge some bubbles to a limited extent, go get takeaway or deliverys so long as there's distancing precautions), a week ago and we've had single digits for about two weeks, including 0 over last weekend! Expectation is level 2 and what that will be will be announced tomorrow. The news really likes to quote overseas papers taking about how amazing and great we are, which feels a bit arrogant given we were lucky in lots of ways 😐
Also, if they aren't mine, then yeah, who cares where they come from! May as well be infinite
@@holctomaz2562 Haha infinite supply
Well, sadly, I know a kid who had a kid in 8th grade, so it's possible. . .
Imagine you walk into into a classroom.
You see a few kids in the front of the class and in a back of the class a bunch of bearded men in suits being like: "Don't mind us, we are just taking notes".
Around 70%. And they publicly give all the right answers faster then any child and then maybe chuckle at their mistakes. Ye, me, a math teacher too, don't ask.
Reminds me of the story "The last lesson " by Alphonse Daudet
That was superintendent inspection day at my elementary school
You're describing Feynman's freshman physics lectures at CalTech.
@@bariumselenided5152 honestly, the kids would do better than the superintendents
(8:55) Intuition for Logarithm
(14:11) Triangle of Power / Relationship between Exponentiation, Logarithms, Roots
(20:11) Product Identity
(24:35) Power Identity
(31:54) Reciprocal
(43:44) Can you have log base zero?
(45:29) Richter Scale
(55:46) log base 2 and base 10
(01:04:50) Change of Base
(01:15:09) Change of Base 2
(01:23:15) Challenge
One of the best ways to get intuition is just plugging in examples
Thanks meight
Thank you! I was looking for something like this
Thanks
When you say that the ones that never learnt logarithms shouldn't be intimidated by the ones who had, it's so wholesome and inspiring, you are by far the best teacher I've seen and watched
In the last question, if you use the other formula, it becomes really quick : logb(a) = 1/ loga(b), so we immediately get the whole expression as log100!(2) + log100!(3) + .... + log100!(100)
Then we use the log(a) + log (b) = log(a.b) and rest follows. Using change of base formula takes more time, this method is quicker.
That's exactly how I went about it, just went to look at the comments to see if someone else did that, not disappointed :D
nice
yea i found that to be much easier. I walked into lecture knowing logs but never know that logb(a) = 1/ loga(b) was a property
Yep, exactly how I did it my head. Using log base 100! seems a little strange, but the pattern works or really nicely.
I also swapped the first priority like your did, noticing that log(2)+log(3)+...+log(100) = log(100!)
That’s the way I saw it, as well. In any case both methods work, and there have been times where the way I’ve gone about solving things either isn’t the easiest to spot, or is more complicated and lengthy to understand...
Awesome lesson. You’re the best maths teacher I’ve come across. Clear, precise, entertaining, fun, enlightening. Keep up the good work!
P
P
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5
I gave my students a link to this live stream this morning. I really hope that they watched this, because next week I might use all of your questions as a part of my test.
That is so nicely cruel. I love it.
I would hope you at least hinted that they should watch it instead of it just being out of the blue. Or that its bonus or the same material was covered in class.
@@Elrog3 it's probably covered in class otherwise they (hopefully) wouldn't link it. I assume the test is about logarithms.
You're an evil genius
As a student myself I approve such evilness.
17:20 One could argue that the radical notation shouldn't even be used at all, since roots are nothing more than some number raised to a fraction
In Ukraine we were taught like this:
ln - log base e
lg - log base 10
lb - log base 2
log - you have to specify base
also tg - tan, arctg - arctan, and other stuff I sometimes can't get used to when I watch lectures in other languages
We used ln for natural logarithm, log for base 10 and lg for base 2; CS studies in Poland
Here in Finland we were taught those same abbreviations for the logs :)
Same in Russia, and all former-USSR
@@CHEpachilo in Soviet Russia, function logs you
Same in Germany
the triangle thingy is what helped me remember what a logarithm is in the first place :D
After Grant told me that log(a+b) didn't have a nice and clean formula for it, I had to do some exploration to see if I could find anything myself, and I have! Mind you, I'm paused at 52:29 so if he already said this later in the video, then my bad for commenting too early. log(a+b) is a pretty weird one to think about, but try to imagine each stretch from the powers of the base being proportionate. For example, just think about the graph of f(x) = log(x) where the base can be anything. Let's say the base is n. Look at the graph from x=1 to x=n. I'm looking at 1 to n because this translates to x=n^0 and x=n^1. If you look how the graph grows from x=n^0 to x=n^1, you'll notice that the graph grows at the same rate between x=n^1 and x=n^2. You'll notice that the y-value's decimal places look very similar at midpoints. You begin to notice that each section of this graph from x=n^(k) to x=n^(k+1) look exactly the same, and that's because it's is (at least proportionately)
So how does this help, intuitively? Let's look at an example of log(8+16) using a base of 2. We know that log(8) = 3, and log(16) = 4. But what about this pesky log(24)? 24 isn't a nice power of 2 so this feels pretty weird, but it just so happens that 24 is the midpoint between 2^4 and 2^5. So the answer of log(24) is going to be between 4 and 5, and we know that the graph of f(x)=log(x) between x=16 and x=32 is proportional in growth rate to that same graph between x=1 and x=2 (because that's x=2^0 and x=2^1). So all we have to do is figure out how deep into the section between x=16 and x=32 we went. We went half way, to x=24. So what's the value half way between x=1 and x=2? Well it's going to be the y-value at x=1.5 because that's half way. Another way of writing that is the y-value of (1+b/a), which is (1 + 8/16), which is 1.5. Take that log.. log(1.5)... or log(1+a/b)... and add it to log(16), and that's your answer. Yes! log(8+16) = log(16) + log(1 + 8/16). I should also note that you can write it the other way around: log(8+16) = log(8) + log(1 + 16/8).
Generally, log(a+b) = log(b) + log(1 + a/b)
AND you can even swap the (a) and (b) on the right side: log(a+b) = log(a) + log(1+ b/a)
Well, a+b = a*(1+b/a) = b*(1+a/b)
(as long as a, b != 0)
great input !
@@gekylafas dividing by zero is fine if you just believe in the heart of the cards.
So I am really still studying the fundamentals here but I am not understanding where the 1 comes from in the re-writing of x=1.5 to log(1+b/a). To be clear -why- is it not log(b/a) instead? or something else?
Because, for example, if you take the log(a+b) where a = 9 and b = 52, you can definitely correctly calculate it with log(1+a/b)+log(52), but in that case the log(1+9/52) = log(1.1730) not log(1.5), so its not like x =1.5 in all cases, x could equal 0.585 or something. I'm sure this is just a basic algebra thing I missed somewhere but I'd appreciate any insight.
@@andrekorenak2417 I think you just need to play around with it in desmos so that what I'm saying makes sense visually. To put simply, I am recognizing that, for example, in log of base 2, that the graph of log(x) looks the same between x=1 and x=2 as it does between x=2 and x=4. And it also looks the same between x=4 and x=8, and between x=8 and x=16. Since each of these sections are proportional, You can actually take a log of something like log(24) and realize that the section of the log(x) between x=16 and x=32 is actually proportional and grows at the same rate as the same graph between x=1 and x=2. Since 24 is halfway between 16 and 32, I can just direct my attention to whatever is halfway between 1 and 2, which is 1.5. That's where I'm getting the 1.5. The results of log(1.5), log(3), log(6), log(12), and log(24) will have the exact same digits after the decimal point, because they are each half way between their respective sections of the graph, and those sections are determined by x=n^0, x=n^1, x=n^2, x=n^3, etc where n is the base of the logarithm.
I used my knowledge of these figures sharing digits after the decimal place to build my formula for log(a+b). Think about the log(24) example. I can rewrite log(24) as log(16+8). First, I'm going to start with log(16), which is just 4. So I know my answer is going to have a 4 in the ones place. Then I need to add the decimal places in, which I have figured to be log(1+b/a). I included the '1' because that's where the graph starts becoming positive on the y-axis, and I'm trying to get a proportionate comparison to somewhere between x=1 and x=n. In this case, n=2 because we're doing log base 2. I then add 'b/a' because that represents proportionately how much further above 1 we need to go. In this case, b/a = 0.5, so log(1+b/a) = log(1.5).
Therefore, log(24) = log(16+8) = log(16) + log(1.5)
Hope that's more clear. :)
1:30:46 best moment of the stream haha. „41 of you want me to come up with a number fact numerical 69, but I won’t“ This really made me laugh😂 Thank you for making such cool streams Grant!
I was looking for this comment:D
ali PMPAINT Yeah, me to haha. But that‘s still a brilliant fun response.
69=9x5 + 9+5 ;)
69= 6x9 + 6+9
When I was a classroom teacher, the number "69" would invariably appear through chance and the class would start snickering, especially if they were middle-schoolers. I used my best poker face and said, "What? What did I say?" and play dumb (I know, I know... not much of a stretch there 8^). As I got more experienced, I made sure 69 didn't pop-up in any of my lectures. But, when it would manage to find it's way into my classroom, on the inside, I was always laughing with my students.
40:10 I have access to small children. Here are the answers I got: (age 4) "6", (age 6) "8", (age 9) "4.5? Wait no, that's halfway between 0 and 9. I don't know. The question doesn't make sense." (Edited time).
These are all great responses! I'm really curious what heuristic the younger ones used... 8 is probably 9-1, plugging the numbers they have into the operation they know that gets a result in between, but 6 is curious, especially as it's actually close. Trying to visualize the number line?
wow.
@Mark Smith I don't understand? giving up on what.. haha on trying?
My brother (8) actually answered logarithmically. I asked him what's between 1 and 100 and he said 10.
@@daemonrec8817 That answer might just be due to our number system having a logarithmic digit length :(
Thank you so much Grant. I'm about to finish my degree in computer science and I just realized log base 2 is also the number of 0's in the binary representation.
25:50 You can see the people working out the details. There was a sudden flash of one answer, but the other 3 were in the ones, sort of even, for a while. Then there was a build on the lower three, but a real powerful build on the leading answer, as if people were finding reasons to exclude certain suspected answers, while the strong build on the leader, people were checking and confirming their strong suspect (the flash). I found this interesting. Determining the calculation time of different paths.
1:07:52 is how I always remembered the change of base formula. Thank you for being the first one to actually help me understand why! I don’t think any of my teachers understood the intuition behind it.
I absolutely LOVE the triangle notation!
Ken Haley @15:35 for those wondering ...
(Something weird is going on with this video ... @10:20 was also temporarily valid!?)
(Thanks Technoultimategaming for noticing something funny was going on with the timestamps between desktop and mobile)
@@MichaelPohoreski
it's actually 10:30
@@technoultimategaming2999 What's REALLY strange is that the @15:35 was the correct timestamp. I viewed it again and @10:20 was the correct one. Now it is back to @15:35 !?
@@MichaelPohoreski
Top 10 cases of the mandella effect
Technoultimategaming LOL :-)
Thank you for teaching me logarithms. Many concepts that you covered had caused me confusion in the past.
You tell you how well you taught me, I was able to work out the final question in my head, although I converted everything to log base 100! and got the same pattern.
I like thinking that logarithms lower the complexity of the input: (exponents -> multiplication -> addition)
It really helped me get through math class, but I don't know if that's the "right" way to look at them.
Wow. Nice pattern observing. Well, personally I treat logs like inverse function of exponent.
logarithm of addition -> ????
would love to see these "lockdown math" lectures like this return! these were so cool! loved the feeling of answering live!
Grant is showing a great way to teach setting students up to be successful USING logs in other math. I love this lecture because years after "learning" logs I was forced to discover on my own this lecture before I could "use" logs. These are great lectures and if I learned in this way in high school math, than later math would have been so much easier. Instead of being guided to discover these properties I was given definitions and memorized rules. In calculus in complex analysis and in dealing with data sets becoming comfortable with this only came about when I was much to old and wrote myself a personal lecture of this sort.
Grants lectures are wonderful. I wish I had CZcams in the 1900s. Each lecture is how I want to teach and how I wish I was taught.
Could you plase do a lecture on conic sections (parabola, hyperbola, eclipse, etc.)
Also if possible please include their general formulae in the XY plane.
It earlier said comic sections not conic sections. Google doesn't understand some things and just autocorrected to comic.
Whoops...
This would be epic
I think you mean conic sections, but I love the idea of a comic starring Parabola, Hyperbola, Ellipse, and Circle as characters.
Forget xy plane, let’s do polar form.
Yes I also agree with the topic
I don't need it... I DON'T need it....
*I NEED IT*
Just 17 minutes into the video, and I am already in love with how you explain!!!
~Just a thankful high school student.
I earn my living by teaching algebra as a tutor. I teach that logarithms represent exponents that have been removed from their base number (though, we keep track of that base number for later.) e.g., log-10 (10^3) = 3
I also think and teach about logs as if they ask and answer the question “What exponent would I need to put on top of the base number to make “The Number of Interest”? (the number inside the log (aka “the argument”)
Using this conception easily helps students see that by “restoring the base” (putting the log as the exponent of the base number), “undoes” the logarithm and delivers the “the number of interest” e.g., 10^[log-10 (1000)] = 10^[3] = 1000
I have a lot more that I teach, but I’ll stop here… this is the major idea I use to help my students understand logarithms.
This is fine when your student (or yourself) is comfortable with exponents. I like having the idea of counting zeroes to fall back on - and have used it when tutoring engineering students in mathematics.
It takes a little more work to get from counting zeroes to manipulating logs than from manipulating exponents to manipulating logs, but the trade-off comes in having a more secure starting point.
@@rmsgrey That only works in base-10, though.
I was thinking this as well. If I were to teach logarithms, I'd probably first drill the idea of inverse functions first.
@@andrewxc1335 It works in any base, provided you're using the same base for your number system as for your logarithms (okay, except unary, which runs into divide-by-zero errors).
And even sticking with decimal notation, logs in other bases are just "count the zeroes and multiply by a constant"
That idea is correct and that's how I was taught them. It becomes more important to understand their identities and where those come from to "unlock their usefulness." I like the way this presents them because it's something I had to "relearn" to become successful in higher math.
I absolutely love your videos. I only made it to diff eq. And lin algebra but i want to study quantum mechanics so I'm learning so much from you. Please please keep making these videos!
If you want to know when the eyeball animation lines all the colors back up, 5:07 is your time.
That spinning logo you've made is really nice!! Perfect!
Grant, your lecture was awesome as usual. You know, usually I leave a "funny" comment under your videos, but... this time was different. When you showed the Richter scale and got down to tsar bomb, I genuinly felt horrified and despite I continued taking notes I could no longer concentrate and eventually stopped writing. Terrifyingly, we know more about war than we know about peace, more about killing than we know about living. And Richter scale clearly showed why japanese named nuclear weapons "cruel bombs". I want to believe that one day nuclear weapons will be completely wiped off the face of the Earth. As Joseph Rotblat said:
"I have to bring to your notice a terrifying reality: with the development of nuclear weapons Man has acquired, for the first time in history, the technical means to destroy the whole of civilization in a single act."
I was also kind of horrified by that section. Good to see I was not the only one.
Why need nuclear weapon? Have you ever heard of 'bio weapon' ?
Ironically nuclear weapons have done more to promote peace than anything else in human history ever has.
I was kind of shocked that Grant would refer to Hiroshima as a neutral factoid. Like it didn't kill so many innocent people. Grant talked about it without any emotion. I couldn't quite focus on the rest of his lecture after that.
Grant's gotta focus on the Maths, like a good teacher - he can't afford to start being emotional or talk about how horrible those things were, though they were indeed horrible, as it's his job to keep the students focused on the Maths.
these type of math videos will never make me feel bored. I want to procrastinate and binge watch these math videos in his channel
A great vedio ... when I was taught logarithms our teacher used to say if you want to compute fast then I need to learn it . So we also had a printed log tables to the base 10. Any number can be broken down to base 10 to power and then the remaining number can be added . That time during the early 90's we were not allowed to use calculators in Indian school... this generated my intrest in logarithms... but once I reached high school and then engineering we never bothered about logarithms other than using it in graphs....
Loving the format of these videos!🤟
My first Uni degrees were in 1973... Your lectures are make a great "remedial maths" series! Looking forward to remedial Lebesgue integration and measures!
Absolutely enjoyable! One of the best videos on the channel.
I love learning from your presentation. You are one of the best math teachers I have ever had. Just curious, but do you also try to discover/work on new math or just teach "textbook" materials.
Thanks for these really useful and easy to follow explanations. Finally was able to get an intuition about logarithms!
This lecture is very helpful especially now that schools have shifted from actual classroom to online platform. This is a big help to students who are presenlty taking math. I am teaching math too in high school and so i came up with a channel to reach out to students. This is such a help. Thanks
For the first question, I'm going to go by the unnamed option E) I had to program a piece of software to automatically determine the right amount of ticks on a logarithmic axis for a given screen size and value range. This is basically teaching a *machine* that *doesn't understand anything* how to use something. IT TOOK ME LITERAL MONTHS TO GET THIS RIGHT and I now know more about logarithms than I ever thought I would have to
on the last question more simple way is to use log a (b) = 1 / (log b (a)),
so it immediately gives log 100! (2) + log 100! (3) + ... + log 100! (100), and this equals log 100! (100!) = 1 :)
Love listening and watching. Marvelous effort.
I had so much fun with the last question! I felt so good that I got the right answer.
Yes I got it in seconds I feel proud
@@mohammadazad8350 My brain is so huge in fact that it actually bent the very fabric of space time wich actively allowed me to have solved the problem before the lecture even aired
@@alexandruchristianapostol975 🤦🤦🤦
I was pretty tickled by my solution to the final problem so I thought I'd share it, step by step. It hinged on the idea that logx(x) = 1
1/log2(100!) + 1/log3(100!) ... 1/log(100!) = log2(2)/log2(100!) + log3(3)/log3(100!) ... + log100(100)/log(100!) = log100!(2) + log100!(3) ...+ log100!(100) = log100!(2 * 3 ... * 100) = log100!(100!) = 1
I did the same thing in my mind.
As the change of base formula is super drilled into your head in highschool, I think the trick you used is a great way to help students remember that 1/log_x(y) = log_y(x)
The triangle notation is actually a better way to teach logs. I think part of the confusion lies in the the notation. In fact I think the same can be said of trig functions as well.
thankyou so much for making this video now my understanding in logarithm is much better. Keep up the good work!
Those lockdown lectures are fanastic！Thank you and hope you would do more helpful ans instructive lectures like those in the future.👍👍👍
OK, I leaned the logarithm in the high school 30 years ago, then I understood (effectively only partially). Then two years ago again (still high school level at 44), but NOW I understand this easy and logical relation between exponent, base and logarithm. A simple triangle helped a lot, and YOU of course! Thank you!
Give back lesson: there is a triangle theory in doing contract work as well, namely: time-cost-quality; you can choose only two of them, the third is the function of those :-)
The amount of intuition in this is amazing
I love your videos. I havnt watched any of these lock down maths because of the long Poll results and banter. Would love to see your take on these math topics that dont take 1.5 hours.
On the topic of the inverse(s) of exponentiation, I think the best way to explain it is similar to explaining subtraction.
Remember back in like 1st grade or whatever when you were first learning math, you learned that because 1+2=3, 3-1=2 and 3-2=1? For exponentiation, the 2 subtraction ones are instead 2 separate operations. 2^3=8, so cuberoot(8)=2 and log base 2(8)=3
I simply love this lockdown math. Its awsome!
finally got a little confidence in logarithm after all the years, thanks a lot !
Please make more of these math lectures even though the pandemic is nearing an end. They help me so much and I don't know what I would do without them.
Hi
OMG! I've never worked with/-or learned logarithms before, and I've always percieved it as some super advanced Einstein-level math-thing.
...But it only took me a couple of minutes of watching this video to understand this perfectly! 🙂
You are a really good teacher! Thanks for the lesson! 😊👍
I really don't like how misconceptions like this are present among so many of the population. I myself fall for it many times, and it only hurts learning and creativity.
@@aviralsood8141 I agree. The fear of something being too complex for me to understand has stopped me from pursuing many interests.
Agreed. I haven't touched maths since I was 16 and passed them with great difficulty. I'm 31 now and interested in all that 'stuff' that made me feel dumb yet I want to know about somehow. Never came across logarithms before either and I'm in awe of how easily I understood them.
@@yos.5684 That's me as well, and I'm also 31 years old! 😂
@@Aerox90 the lost generation, so they say, hahaha
I mostly understood logs but the change of base formula always felt like magic to me, it makes a ton more sense now!
Wonderful class! 69 and not even a laugh, this guy is strong.
I'm getting the impression that a solid understanding of exponention would be a helpful thing here.
that was previous lesson in same series
@@weksauce, #5 was imaginary interest rates. I haven't watched the whole thing, but I don't think that exponention was covered.
@@robertwalker-smith2739 it was covered
@@user-or2gl9sq5d , thank you, I'll give it a look.
Went through the entire video. Fascinating exploration of imaginary and complex numbers, but nothing about exponents.
This came out just in time for my final tomorrow, I already understand them well but this is good review of the material 👌
How'd it go? if you remmeber
Thanks a lot for yet another incredibly engaging episode! You've probably thought of this already, but perhaps you can show the live answers as vertical bar charts on the left of the screen so they don't cover you while you're talking
Thank you, Grant. I wish I had learned it this way from the start.
In the COVID-19 Exponential video you made reference to the lag relationship between S-Korea and Australia and how we (AUS) were just 42 days behind S-K, not necessarily doing better. I watched the video on the 10th of March and then on the 30th March and we were at the time in exactly the same place as Korea at the same time after 100 cases, as predicted by the Maths.
I even showed that video to a class of 12 year old's and they understood the urgency of taking strong action, early.
I found that a good way to think of what it means to swap the base of the logarithm is actually that we are counting how many times the base has been multiplied with whatever is in the brackets.
So for example Log5(125).
This = Log5(5 * 5 * 5) and is therefore 3
Okay, youtube do you want to explain how I ended up here!
So I fell asleep watching youtube and woke up to this video.
Last question is really Amazing ,
I have tried and thought Oh Wow I solved it!!!!
Change of base gets me quicker
⏩ And Ans came up easily but gave me an insight and that i want from this lecture
Thanks 3b1b , Thanks Grant for born in here
🙏 thanks
I think the best part about integer common logs, is all you really need to do is memorize all the ones that are prime (2, 3, 5, 7, 9 etc)and then you can just reason out the rest in your head.
Since adding log(2) and log(2) gets you log(4), log(2)+log(3) gets you log(6), log(2) + log(9) gets your log(18), etc. And just add one for every zero you tack on the end of the answer. So log(600) is just roughly 0.301 + 0.477 + 2 = 2.778. :D
That's how I do it anyway. :)
The "max" property of logs is related to the link between "addition" in the log semiring and the tropical semiring.
these videos should have over dozen of millions of views, many students who are not comfortable with English might benefit if such videos have high quality local language translation, i bet if in school or college i would have watched these series i would have better at maths and could have build deep interest, the videos make fall in love with mathmatics, never too late though
I use logarithms all the time in my job; specifically dB. After a while it becomes effortless to swap between linear measurements and their (approximate) logs in your head. This skill becomes useful in daily life because multiplication and division become simple addition and subtraction, which again... you can do in your head.
Thank you for this. Just what I needed for my discrete math class to make sense of things. I went to high school in Texas, and I feel like my school really did not do this subject any justice.
I needed all these lessons a year a go
Thank you Grant, this is really helpful for a student like me! :)
Thank you very much for al your effort, Grant!
Yeah, and having a good teacher shouldn't be taken for granted
After looking at the challenge puzzle, I was like holy cow, but after 10 seconds I got the answer.
Thank you 3B1B❤️❤️
Grant, Thank you so much ! if you can do more of these basics video's It would be great!!!
_3b1b throwing pearls to the swine:_
"Eat, there's plenty more" 😂
'1' is probably the most common answer to mathematical questions, and is always a nice guess when the math teacher asks what number something adds up to or is equivalent to.
In Academic Bowl, we joked that the answer to the math problems was either 1 or 0.
As they say, 0, 1, and infinity are the only numbers you can use without a justification.
Enjoyable video to watch and clear up some questions as well
In computer science (in particular growth rate estimation) it is usually irrelevant which base is used since Logb x / Loga x is a constant, and constants are usually discarded.
Thank you, test about logarithms tomorrow and this was a huge help! Also, what kind of pen is that? Is it a standard ink pen? (sorry my focus is a bit all over the place)
It looks like it was a fun lecture. I use logarithm and exponential math all the time because I work in the field of lidar. I think you alluded to it but this sort of math is magic for many people and thus they don't understand exponential growth found in pandemics as we see. finance, sound levels, anything with large growth and/or dynamic range.
When I first worked with logarithmic expressions, I would translate it to "Okay, 3 raised to the what power is equal to 81." And I must say, it makes the meaning of the log function easier to comprehend.
I could listen to that Pause-and-Ponder music on repeat all day...
Many months late here, but if you look up 3blue1brown on spotify, there's a whole album/playlist by the artist who wrote the pause and ponder music :)
amazing lesson!! thank you!
So happy to see the triangle of power again!
triangle of truth and wisdom
I finally understand them an in intuitive level. A logarithm's answer is basically how far a "step" is within the current magnitude. Meaning the current power of its base as the magnitude. So 10100 is 100 into the magnitude of 10,000, which is approximately 1/100th, but since logs have growth on an exponential scale, the actual "step" is just under that, at about .004 or .005 instead of 0.01. Eventually I'll grasp that intuitively to get the math, but now that I understand it's "steps" within the magnitude of the base, when to use them makes so much more sense.
I got A's in math but only b/c I knew the formulas. I had to re-teach myself math just to get it intuitively... and it's so much fun now. As a programmer, i get to use it and know why/when
the log's as inside-out exponents absolutely blew my mind.
bruh thats the deffinition of a log tho
@@karlkfoury2213 lmfao ikr
This was really helpful :) thanks!
Cool video as always! Logarithm seems to be a difficult concept as it involves rotation of e on y=x. But still, it is a very cool topic that is closely related to our real life examples! Cool!
Please make one video on inverse trigonometric functions
I haven't imagined it and have mugged it up.🙏🙏🙏🙏
You should break out a old version of the CRC Standard Math Tables and show how engineers did their math before calculators by using log tables. Or sliderulers.
zengargoyle Would be a great segue to introduce Newton's Method and quadratic convergence!
Interesting. Yesterday I had to leave mid-stream because it was almost 22:00 in my timezone and still had to eat dinner, so it was very late, and now I watched the rest. Something I remembered during this lecture is how that time I was on the toilet not having anything else to do, I derived the change of base formula. It was quite satisfying...
You are formidable! Amazing! You are totally wonderful!
Loved this!
Thank you for this video, finally at age 35 and as a math students I understood it.
53:20 each time tnt increases by a factor of 32. One more of the base fits in to the () so the log goes up by one.
"log₂" is often written as "lg". So I read "log" as "log₁₀", "ln" as "logₑ", and "lg" as "log₂"
We used to write "lb" for "log₂", with "b" as in "binary". :-)
@@cannot-handle-handles And you didn't have some people constantly misreading it as "pound"?
@@ShadSterling I guess it was clear both due the syntactical difference ("lb(n)" is probably not "pound") as well as because of the computer science context. :-)
I think in your notation of the relation between the base, power and the value, the power and the value should swap places. So, you can say that 1000 can be constructed by these two numbers 10 and 3.(would really welcome some feedback on this proposition)
Awesome Lecture! I finally understood logarithms!
9:02 addition and multiplication both have commutative property, i.e., a+b=b+a=c and j×k=k×j=l. Thus the same operation can be used to find any of the operands. b=c-a, also a=c-b. Similarly, j=l/k and k=l/j.
But exponent doesn't work that way. (x^y) is not equal to (y^x), thus different operations are used to find these operands.
*Logarithm is used to find exponent and root is used to find base.*
Wow have just started the video and it's wonderful
My alg II teacher kinda just skimmed over all these properties and told us that’s how it is… this is so much more helpful!
50:00 Akshually - IIRC they DID build the Tsar Bomba to go off at 100 kt, but it was kind of a "fizzle." Sort of the opposite of Bravo. With Richter, we double the power with every increase of 0.2 in the scale. Another popular usage of log is mapping "hockey puck" growth such as population, which diminishes earlier effects like the Bubonic Plague, Three Kingdoms Wars, Khanate invasions, two World Wars and Spanish Flu etc. over which log(population) at least shows noticeable dents.