Wuck. play.google.com/store/apps/details?id=org.flammablemaths.Wuck Train your Complex Number Expertise by trying out Brilliant! =D brilliant.org/FlammableMaths Check out my newest video over on @Flammy's Wood ! =D ua-cam.com/video/_sL6AKAcBTY/v-deo.html log of a negative number: ua-cam.com/video/FjfIeZN1CUU/v-deo.html
Hey, I just wondered: Is there a concrete reason why you prefer wirting "log" for the natural logarithm instead of "ln", even though "ln" seems to be the most conventional notation?
@@slawomirdrapinski4538 Most people use Ln() to make calculations easier but some people (like Flammy and me) uses natural log instead. I think he is asking if there is a reason for that. And if I couldn’t express myself well enough here is an example x^y=z Most mathematicians will take Ln of both sides to be able to use y, but the base of the logarithm really doesn’t matter. Instead of Ln, you could use any other base for e as Flammy said. But using Ln for this purpose is kind of more universal
@@berenozgenc8422 in school we learned with the log with the base of 10, instead of ln, but that was just because its easier to put in into the calculator cause the default in calculators is normally log with the base of 10
I think that the natural logarithm and exponential function with e as the base are extremely notorious in calculus and not only calculus, hence people often use exclusively those and take it as their default logarithm lol
@@blackhole3407 Not quite. For example: (2 + 6i)/(2i) = 1/i + 3 = 3 - i Which is still imaginary. You'd only end up with a real solution this way: Suppose two complex numbers z_1 = a + bi z_2 = c + di Then z_1/z_2 = (a + bi)/(c + di) = [(a + bi)/(c + di)] * [(c - di)/(c - di)] = (ac - adi + cbi - bdi²)/(c² - d²i²) = (ac + bd - adi + cbi)/(c² + d²) The denominator is always real. The enumerator is only real if ad = cb For example: 4*1 = 2*2 (4 + 2i)/(2 + i) = [(4 + 2i)*(2 - i)]/[(2 + i)*(2 - i)] = (8 - 4i + 4i - 2i²)/(2² - i²) = (8 + 2)/(4+1) = 10/5 = 2
I like the log of negative 69 of 20730897752653674714720723427459000889249915529600981530433365335188589206775527139229601995115836043535786629580792144773078426776834268298332187236818042380226849443884860369688406406660118018751041554543095806670784324017067690408791078125463951378030499174512211021762053899146321811754326676200848317668615746032791477810189370765796872015454208726535891065392365497780680934294765890614462433230434642019850210194574941837149904506668092623531566731463976957855738022148581771099684223664263637368004862059648627935705330725186314285961032283586277966145966280929918887266909890820024385375444923126652775589102263540978186901034212346494403140899551856996521257241285133877814522994967358822224685926377660467871022924275654082181950373765807211473562917453950351601 It's a pain to write that out, but yes, that's way too many digits for anyone to remember that number in their head. It's so big it contains the answer to the question itself. And if you take that number and put it in google search, you'll get 1 match, a youtube playlist with the name :-) Oh and the answer of the math problem is 420. Oh and it has 773 digits.
The problem with utilizing logarithms with real bases that are negative is that, in relying on the complex logarithm, they remain ill-defined. The complex logarithm is not a function, so in a regard, it is not well-defined, and the problem with using the concept of branch cuts is that properties that the logarithm was intended to have definitionally, such as Log(z·w) = Log(z) + Log(w) and Log(z^w) = w·Log(z), are no longer true in general. You can talk about these properties being preserved in the context of set equations, where the complex logarithm is treated as a multiset of complex numbers, rather than as a function of complex numbers whose output is a complex number. However, mathematicians have studied this approach, and this formalism is completely useless computationally and meaningless in the context of abstract algebra and theory of equations. The approach is powerful in sheaf theory and the theory of Riemann surfaces, but these are mathematical disciplines most people will never even encounter, and they do not contain concepts that would ever motivate going to unnecessary lengths to define something like the logarithm with negative base, because the latter concept is purely a computational tool, not a theoretical one. It is for this reason that you never see mathematicians talking about logarithms of negative base in their writings, or about complex exponentiation whete both the base and exponent are complex and non-real. The fact that the exponential function in the complex numbers is not injective numbers means there is no well-defined, consistent way of computationally dealing with logarithms at that level. What makes this even worse is that the complex logarithm cannot even be generalized to algebraic structures beyond or outside the complex numbers, even though you can generalize the exponential function to such structures. Since there are already many suitable replacements for this concept of the complex logarithm that does not try to force notation into doing things it cannot do, even if we want it to, I always have found it rather unhealthy to try to force expressions such as log(-5, 6) to make sense. I am the kind of person that will only use notation such as x^n if n is an integer, and instead of using a^x for a > 0 as an abbreviation for exp[ln(a)·x], I will rather explicitly write out the latter. This may seem overly nitpicky and pedantic, but I think this is a healthier way of doing mathematics. Having inconsistent notation is no way of doing mathematics, and the false sense of alleged convenience that is not actually there, in return, is definitely not worth it. So in summary, if you really want to make life difficult on yourself as a mathematician, you technically can use complex numbers and define logrithms with negative or complex bases with negative or complex arguments, but the only thing you are actually accomplishing is making the logarithmic concept no longer behave as it was intended to, making the notation clunky, not very consistently, and unecessarily convoluted, and not creating a tool that is theoretically appropriate or computationally useful. So honestly, why bother? There are already alternative ways of dealing with all of this, without needing to even the logarithm concept. At least, that is my take on it. I am not discouraging the act of trying to discover new ideas and exploring concepts heuristically. But sometimes, the ideas being discovered are bad ones, and eventually abandoned by mathematicians for good reason. This is one of them.
The contrast between how silly the content of the video is and how involved and serious your comment is is genuinely funny on a level I find hard to describe. It doesn't help that Papa Flammy responded in the most whimsical way, either.
I once missed out on an 100% on a log test because I used a similar OP logarithms law/substitution to solve a 9 mark question in two steps (teachers mad, deducted points)
papa flammy you should make a video on the fractional derivative of the riemann zeta function and the dirchlet eta function if im not mistaken your master's thesis was exactly that, it'd be cool if you made a video on that cuz fractional calculus = kewl
Could i just take it and manipulate to get into the principal log using exponentials? (-5)^z = 6 And taking the principal log both sides z Log(-5) = Log(6) z = Log(6)/Log(-5) (6 is is a real number, namely, it has 0 π degrees into the complex plane,considering -π
Ich almost habt keine Ahnung about what you said in that previous video, but fortunately there was some math in it, and that was something that I could understand ;-)
So if I put log-5(-5) into my calculator I'll just get an error? Is this supposed to make sense or do I just have to accept that mathematicians said fuck negative bases?
I thought you should rationalize the denominator to get [ln(6)ln(5) - i ln(6)pi(2k+1)]/[((ln(5))^2-(pi^2)*(2k+1)^2] I don't think that can be simplified more but it is in a nice a + ib form
If pi = vaccinated, e = unvaccinated how big does the circle of vaccinated people need to be, in order to achieve herd immunity based on the world population, without violating the value difference between pi and e?
Wuck. play.google.com/store/apps/details?id=org.flammablemaths.Wuck
Train your Complex Number Expertise by trying out Brilliant! =D brilliant.org/FlammableMaths
Check out my newest video over on @Flammy's Wood ! =D ua-cam.com/video/_sL6AKAcBTY/v-deo.html
log of a negative number: ua-cam.com/video/FjfIeZN1CUU/v-deo.html
Still waiting for wuck to install :/
Nice
based
3 hours wtf
Wow that was really cool!
On a serious note who also watches Dani?
I just learned about logarithm today and this recommended
Lol
Didn't even learned, ik it's kinda hard
@@DatBoi_TheGudBIAS but it's not that hard. you just need to find the value of da exponent
Let me give you an advice, change your mindset nothing is hard, untill you try it, there is no wall that is unreachable
What grade are you in?
First rule of math:
If you see a "unsolvable" problem, it has a complex solution.
if it is negative base.. does that mean that log is un-based = cringe?😳
No, I think it means it's acidic, because acids are the opposite of bases.
Nikatgeh
Hey, I just wondered: Is there a concrete reason why you prefer wirting "log" for the natural logarithm instead of "ln", even though "ln" seems to be the most conventional notation?
He wrote ln for the natural log and log for a logarithm with a different base
@@slawomirdrapinski4538 Most people use Ln() to make calculations easier but some people (like Flammy and me) uses natural log instead. I think he is asking if there is a reason for that. And if I couldn’t express myself well enough here is an example x^y=z
Most mathematicians will take Ln of both sides to be able to use y, but the base of the logarithm really doesn’t matter. Instead of Ln, you could use any other base for e as Flammy said. But using Ln for this purpose is kind of more universal
@@berenozgenc8422 in school we learned with the log with the base of 10, instead of ln, but that was just because its easier to put in into the calculator cause the default in calculators is normally log with the base of 10
I think that the natural logarithm and exponential function with e as the base are extremely notorious in calculus and not only calculus, hence people often use exclusively those and take it as their default logarithm lol
@@timonbubnic322 Same
11:23 This can't be a definition of pi, because we need to define a logarithm with negative basis first, and to do it we need a pi.
thats not how it works.
Listen here you little s**t
Now all we need is a generic expression for "log to the base (a+bi) of any complex number (c+di)"!
Thanks to this video, we have proven that pi is not just transcendental - it is imaginary.
I think imaginary/imaginary=real because the i's cancel out
@@blackhole3407 Not quite. For example:
(2 + 6i)/(2i)
= 1/i + 3
= 3 - i
Which is still imaginary. You'd only end up with a real solution this way:
Suppose two complex numbers
z_1 = a + bi
z_2 = c + di
Then
z_1/z_2
= (a + bi)/(c + di)
= [(a + bi)/(c + di)] * [(c - di)/(c - di)]
= (ac - adi + cbi - bdi²)/(c² - d²i²)
= (ac + bd - adi + cbi)/(c² + d²)
The denominator is always real. The enumerator is only real if
ad = cb
For example: 4*1 = 2*2
(4 + 2i)/(2 + i)
= [(4 + 2i)*(2 - i)]/[(2 + i)*(2 - i)]
= (8 - 4i + 4i - 2i²)/(2² - i²)
= (8 + 2)/(4+1)
= 10/5
= 2
@@Schaex1 imaginary Only referes to an imaginary part. Not the whole complex number.
Thus ad and cb are always zero. And hence equal
@@Schaex1 that would be for complex/complex not imaginary/imaginary no?
Explanation is nice. Thanks for amazing content
Only German speakers will understand why 6 is a funny number
Sechs
I see it as the first half of a funny number
They also know what comes between fear and sex: fünf!
haha sechs
That's not true. Swedish, Danish and Norwegian speakers will as well.
The first math video of the year.
I like the log of negative 69 of 20730897752653674714720723427459000889249915529600981530433365335188589206775527139229601995115836043535786629580792144773078426776834268298332187236818042380226849443884860369688406406660118018751041554543095806670784324017067690408791078125463951378030499174512211021762053899146321811754326676200848317668615746032791477810189370765796872015454208726535891065392365497780680934294765890614462433230434642019850210194574941837149904506668092623531566731463976957855738022148581771099684223664263637368004862059648627935705330725186314285961032283586277966145966280929918887266909890820024385375444923126652775589102263540978186901034212346494403140899551856996521257241285133877814522994967358822224685926377660467871022924275654082181950373765807211473562917453950351601
It's a pain to write that out, but yes, that's way too many digits for anyone to remember that number in their head. It's so big it contains the answer to the question itself. And if you take that number and put it in google search, you'll get 1 match, a youtube playlist with the name :-)
Oh and the answer of the math problem is 420. Oh and it has 773 digits.
wtf......this went over my head
Ohl
The problem with utilizing logarithms with real bases that are negative is that, in relying on the complex logarithm, they remain ill-defined. The complex logarithm is not a function, so in a regard, it is not well-defined, and the problem with using the concept of branch cuts is that properties that the logarithm was intended to have definitionally, such as Log(z·w) = Log(z) + Log(w) and Log(z^w) = w·Log(z), are no longer true in general. You can talk about these properties being preserved in the context of set equations, where the complex logarithm is treated as a multiset of complex numbers, rather than as a function of complex numbers whose output is a complex number. However, mathematicians have studied this approach, and this formalism is completely useless computationally and meaningless in the context of abstract algebra and theory of equations. The approach is powerful in sheaf theory and the theory of Riemann surfaces, but these are mathematical disciplines most people will never even encounter, and they do not contain concepts that would ever motivate going to unnecessary lengths to define something like the logarithm with negative base, because the latter concept is purely a computational tool, not a theoretical one. It is for this reason that you never see mathematicians talking about logarithms of negative base in their writings, or about complex exponentiation whete both the base and exponent are complex and non-real. The fact that the exponential function in the complex numbers is not injective numbers means there is no well-defined, consistent way of computationally dealing with logarithms at that level. What makes this even worse is that the complex logarithm cannot even be generalized to algebraic structures beyond or outside the complex numbers, even though you can generalize the exponential function to such structures. Since there are already many suitable replacements for this concept of the complex logarithm that does not try to force notation into doing things it cannot do, even if we want it to, I always have found it rather unhealthy to try to force expressions such as log(-5, 6) to make sense. I am the kind of person that will only use notation such as x^n if n is an integer, and instead of using a^x for a > 0 as an abbreviation for exp[ln(a)·x], I will rather explicitly write out the latter. This may seem overly nitpicky and pedantic, but I think this is a healthier way of doing mathematics. Having inconsistent notation is no way of doing mathematics, and the false sense of alleged convenience that is not actually there, in return, is definitely not worth it.
So in summary, if you really want to make life difficult on yourself as a mathematician, you technically can use complex numbers and define logrithms with negative or complex bases with negative or complex arguments, but the only thing you are actually accomplishing is making the logarithmic concept no longer behave as it was intended to, making the notation clunky, not very consistently, and unecessarily convoluted, and not creating a tool that is theoretically appropriate or computationally useful. So honestly, why bother? There are already alternative ways of dealing with all of this, without needing to even the logarithm concept. At least, that is my take on it. I am not discouraging the act of trying to discover new ideas and exploring concepts heuristically. But sometimes, the ideas being discovered are bad ones, and eventually abandoned by mathematicians for good reason. This is one of them.
+1
I ain’t reading all that
The contrast between how silly the content of the video is and how involved and serious your comment is is genuinely funny on a level I find hard to describe. It doesn't help that Papa Flammy responded in the most whimsical way, either.
why for example, Log[-2,(-2)^(3)] doesnt give 3 ? Like I understand going through the complex world but shouldn't it be the point of log ?
depends on the branch
log[-a](b) = ln(b)/ln(-a) = ln(b)/(ln(a) + ln(-1)) = ln(b)/(ln(a) + i*pi*(2k+1)) = ln(b)/(ln(a)^2 + pi^2*(2k+1)^2) * (ln(a) - i*pi*(2k+1))
It's only fitting that UA-cam would suggest translating this to English
I once missed out on an 100% on a log test because I used a similar OP logarithms law/substitution to solve a 9 mark question in two steps (teachers mad, deducted points)
that's stupid
That teacher should get demoted for abominable stupidity.
“whAlecUm back to a new video” -papa flammy every video
Wait why are you working with Logs on your main channel? I thought that you made Flammy's Wood for that?
:^)
My teacher pronounces ln as lawn and it sounds pretty cool and fun to say
xD
At this point, one of the main things I learned is that Flammable has incredibly clean black boards.
indeed :^)
Can you do more derivations/proofs? Amazing video btw!
Username checks out
Whenever I want to study mathematics, I first watch some of your videos to get some motivation❤️❤️thanks bro
Greatly enjoyed this one ... Many thanks ... Cheers ...
negatively nice
PAPA IS BACK!!
Omg, is Wuck a reference to Muck (im assuming) from Dani also because of the similar interview thing?
papa flammy you should make a video on the fractional derivative of the riemann zeta function and the dirchlet eta function if im not mistaken your master's thesis was exactly that, it'd be cool if you made a video on that cuz fractional calculus = kewl
We need new funny numbers, and 6 should be one of them
Well... imaginary, irrational and transcendental bases?
Could i just take it and manipulate to get into the principal log using exponentials?
(-5)^z = 6
And taking the principal log both sides
z Log(-5) = Log(6)
z = Log(6)/Log(-5)
(6 is is a real number, namely, it has 0 π degrees into the complex plane,considering -π
that's actually really cool
Exactly what I was looking for.
How can I get good in maths like you please tell
What do you mean when you say, principle branch?
I guess the angle is between -pi and pi
11:00 - 11:15 Nice middle finger lmaoooo
Where did you find this marvelous mandelbrot set poster behind you
?
Ich almost habt keine Ahnung about what you said in that previous video, but fortunately there was some math in it, and that was something that I could understand ;-)
Maybe I missed something but what was the point of using ln in this case? Doesn't everything you did work with any base log?
I know I am a bit late with my comment, but we need to use ln, because otherwise, the polar form of -1 won't be useful (as it is base e).
I heard "in our case" as "in all case" at 4:40 and got very concerned for a bit there.
So if I put log-5(-5) into my calculator I'll just get an error? Is this supposed to make sense or do I just have to accept that mathematicians said fuck negative bases?
There are infinitely many answers of which many are complex
Papa! Flammy underwear for 2022 merch? 😎
yeye
What about a complex, quaternionic or other higher dimensional base?
the Chad Wuck vs the Virgin AAA game
"log -69 (e)" the thumbnail is wild
Well, I guess Goggins isn't the only one carrying the logs
I dont understand any of this but somehow i still find it interesting to watch
I thought you should rationalize the denominator to get [ln(6)ln(5) - i ln(6)pi(2k+1)]/[((ln(5))^2-(pi^2)*(2k+1)^2]
I don't think that can be simplified more but it is in a nice a + ib form
Yeah log that thing from your other channel-i totally know all about it
vorallem wenn man dann (-1)^pi betrachtet sieht man das es einfach eine komplexe zahl ist
Strange but irrefutable identity for the omnipotent Pi.
Gracias man.
This shirt emanates pure Sigma Chad Energy
Now do -420 and -666
haha, this is such a BASED video
Papa Flammy.
being early is the best feeling
I expected better from you...
logbase -69 of 420 😤
At this point i dont know if everytime you mention wuck you are referencing dani or its just a coincidence
Ich liebe es wenn sein deutsch Mal rausrutscht xD
6 is a prefect number 😀.
that's a pretty weird definition of pi i admit haha
:D
logarithm with base "yo mama" when /s
that is fucking cool
I clicked this video because the thumbnail made me viscerally upset.
Floor{[ln(2)]*100}
-nice
This is good! The video is good!!
But still not as good as WUCK! 🙄
now do complex base
me who don't even know how log work:
0:45 jfc
"Pah" ;-;
Writing "ln" is easier then "log" what do you mean XD
writing ln sucks
@@PapaFlammy69 Did you also used to always write I (i) n instead of l (l) n
I just realized "logarithm" is an anagram of "algorithm".
This realization is useless.
Wuck
MOM GET OUT AM BEGGING FOR MONEY
:D
I've been taking a break from youtube for years lol
Nice
nice
YOURE SO CUTEEEEEE
hehe funny number
Imma be honest i saw 69 thats the reason im here
If pi = vaccinated, e = unvaccinated how big does the circle of vaccinated people need to be, in order to achieve herd immunity based on the world population, without violating the value difference between pi and e?
69… nice.
Noice
The thumbnail is not nice
y doe?
@@PapaFlammy69 -69 is the opposite of 69
First
Yes I approved.
Your stuff is ok but for me the “humour” is irritating and unnecessary
WTF is AAA Gaming , all my homies play『 W U C K 』