Logarithm Fundamentals | Ep. 6 Lockdown live math

Anybody have a link to intro music?

I need to know about mathematics! I am not a part of your analytics ffs. Good-bye.

Well, I'm watching this again as I just taught my students about logarithmic today. Just wish we have time to approach the logarithmic like this, instead of throwing at them a bunch of definitions, properties and exercises.

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!

3 is halfway to 9 because of the proportionality of 1 to phi.

my biggest wow moment is :


c^y = b; Log_c(b) = y
b^x = a ; Log_b(a) = x
c^(yx) = a; Log_c(a) = yx

thus,
Log_c(b) * Log_b(a) = Log_c(a)

and,

Log_b(a) = Log_c(a)/Log_c(b); where c is any base except 0.

Thank you, Grant. I wish I had learned it this way from the start.

to log(a*b) = log(a)+log(b)

Doesn't this break at log(0)?

Awesome Lecture! I finally understood logarithms!

finally got a little confidence in logarithm after all the years, thanks a lot !

Why am I watching this at 4AM XD
Anyway brilliant lesson, I understood everything, thank you!

the difference between logs and root as i likw to see it is that while logs are a reciprocal to exponenetials. roots aree the receprocal to polynomials x^n as oposed to n^x

lol quelqun just means someone in french

Philosophy of Education hinges on the Socratic Method of questioning the importance of answering questions, so "Define your Terms" has a sustained urgency in finding sense-in-common cause-effect access to unlearning our presumptions and what is required is to continually update, collect and collate the correspondence of Terms in practice, ie application of elemental e-Pi-i sync-duration resonance =correspondence, truth in/of Principle.

amazing lesson!! thank you!

I didn’t see a small child in the required materials but I was wondering where I fit with 4.5 as my “intuitive” answer?

I seem to see a similarity between log(a*b)=log(a)+log(b) and the exponential function, where you add angles and it becomes multiplying their corresponding complex numbers on the unit circle... I wonder if there is a deeper connection there?

not many times can you hear the words "thank you, Karen" uttered in the wilds of les internets...😆

one theory as to why logs are one of the hardest topics to teach in math: our brain's factory default is to compare numbers logarithmically, and all the math education up until the introduction of logs is training us to STOP thinking logarithmically... and so logs go from being the way the brain wants to think about numbers (for evolutionary survival reasons: 1 more lion showing up makes a much bigger difference to survival chances if you are up against 10 lions than if you are up against 100) to only thinking in logs when comparing large numbers in a conversational setting (we do like comparing things in terms of how many times larger they are), to then having to deal with a bunch of properties that not only don't quite grok with the math we have been trained to do, but even go so far as to feel like cheating (when tutoring people, I will sometimes joke that the power property of logarithms is one of the few instances in math where you are allowed to cut and paste (the only other one I can think of is variable substitutions... because dummy variables tend to make everything easier)

i like how he waited for the spinny to loop all the way around at the start

One mega tet [TNT equivalent tonnage] of energy actually isn't that much when you're comparing it to the size of the earth.

It's funny how the logarithms turned out to be essentials in all areas of science,if we remember that at the beginning it was only the very pragmatically need to compute the multiplication that motivated Napier to invent it some 400 years ago....

One humble historical remark: Napier ( a Scottish genius) invented the logarithms at the beginning of the 17 century( aproximatively).His motivation was very pragmatic: at that time it was really hard to compute the multiplication of large numbers!!!!! So he invented the Logarithmical Tables.Let s explain it... Napier calculated log1,log2,log3,....log 10000000....( Log in this context means log basis 10).He noticed that: log(x *y)= logx+ log y means that x*y becomes easy if we could compute logx+ logy... Indeed using the Logarithmical tables, multiplication is reduced to addition, which is much easier!!!!!

Loved this!

Regarding the relationship between log( a, b) and log( b, a):

Multiply the two and use n * log( x) == log( x ** n):

log( a, b) * log( b, a)

== log( a, b ** log( b, a)) == log( a, a) == 1
== log( b, a ** log( a, b)) == log( b, b) == 1

Regarding the inverse question: Addition and multiplication are commutative, and that is why each has only one inverse function: E.g.,

a + Inv( a) == Inv( a) + a == 0; Inv( a) == 0 - a

Exponentiation is not commutative. 3 ** 10 != 10 ** 3. Here, the side of the operator matters. There is no one Inv function that satisifies

Inv( a) ** a == a ** Inv( a) == ?

At least, I don't know of such a function! So here we have a left-inverse and a right-inverse:

InvL( a) ** a == j ; InvL( a) == j ** ( 1 / a) == "a-th root of j"
a ** InvR( a) == k; InvR( a) == log( a, k) == "log base-a of k"

I use j and k here because we have no one identity (i) for exponentiation:

a ** i == a implies i == 1
i ** a == a implies i == a ** ( 1 / a)

As

Math conan

Thank you Grant, this is really helpful for a student like me! :)

Answer of that question is on thumbnail

at uni. this solidified, reconsolidated, and clarified. THANK YOU

0^0 = 1 😀

(log₀(x)=ø if x≠0) and (log₀(x)=D if x=0)

For the last question I came up with that the final question would be "log base 100! of (100! )". Isn't that correct? But I guess that's 1?

Enjoyable video to watch and clear up some questions as well

The Japan March 2011 earthquake at 9.1 had the energy of ~890 x Tsar Bombas (using base 31.62)
which, depending on rounding errors matches with an increase in +2 of the Richter corresponding with an increase of x1000 in TNT

Algorithmic and logarithmic complexity at operations research mesh matrices applications

The introductory “The lesson will start shortly “ is very tedious. Several minutes of music and a rotating image is over the top.

Another note on how to notation of logarithms. I've learned that ln(x) is natural logaritms eg. base e based, lg(x) is 10-base, lb(x) is 2-base and log(x) is just arbitrary used to describe laws that are not base dependent. Subscipts are used when denoting other than 2, e or 10-based logarithms and when stating laws changing bases of logarithms.

Not meaning to criticise or insult in any way :-)
Last one was actually quite easy (really, I didn't even know about logs until this lecture 😅)if you knew the reciprocal identity, after applying that and the identity that log(a) + log(b) = log(ab), it simplifies to log100!(100!) = 1 🙂🪄
Also, in the final solution instead of expanding the denominator, we could just simplify the numerator, it would make writing easier and save time :D

Hands down, Grant is THE BEST teacher anyone can ever have!

If (log base a of b = x ) is equivalent to ( a exp x= b), why the formula for change of base ( log base c of b x log base b of a = log base c of a)
does not work if you multiply the equivalent exponentials in lieu of multiplying the logarithms ?

we quickly glossed over logarithms in chemistry for calculating pH levels without getting a good explanation of how they actually work lmao. Luckily a friend gave me a good explanation.