Proof: log a + log b = log ab | Logarithms | Algebra II

Proof: log a + log b = log ab | Logarithms | Algebra II | Khan Academy

Рет қаралды 374,057

16 жыл бұрын

Proof of the logarithm property: log a + log b = log ab
Watch the next lesson: www.khanacademy.org/math/alge...
Missed the previous lesson?
www.khanacademy.org/math/alge...
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
/ channel
Subscribe to Khan Academy: kzfaq.info_...

Пікірлер: 75

@MyCheesebrain 12 жыл бұрын

Sal: Hello Me: oh we're getting saucy today

@daemperor2263 8 жыл бұрын

I find these videos to be surprisingly amusing when I pretend Sal is a chameleon. "Let me switch colors, I think that keeps things interesting." "I will never run out of colors. I have infinite colors!"

@ultimatepirate9589 7 жыл бұрын

"i have infinite colors i'll never run out of colors" XD had me rollin

@alexswift2k847 6 жыл бұрын

ultimate pirate lol

@kkngenomesho7744 6 жыл бұрын

that 'Hello' was sketchy AF

@armangrigoryan6329 5 жыл бұрын

yep

@AmbiambiSinistrous 12 жыл бұрын

When he says "hello" at the beginning, I was half-expecting him to start off into "Does your man look like me? NO. Can he smell like me? YES..."

@AmbiambiSinistrous 12 жыл бұрын

"... the logarithm, when you evaluate it, really IS an exponent..." O_O This is the most useful thing I've heard all week. THANK YOU SO MUCH. (I know it makes sense, it just didn't really click until he said it...)

@offrow 4 жыл бұрын

I was wondering why the quality was so awful, then I realized the video was released in 2007.

@SartajKhan-jg3nz 5 жыл бұрын

I am watching the video on 2018. Sal sounded soooo different back in 2007!!!

@Hoodesrb 11 жыл бұрын

"Let me switch colors, I think that keeps things interesting" Thats so true when you think about it, yet so simple.

@nocturnalvisionmusic 6 ай бұрын

Loved that "hello" intro and 2:47 "let's keep going and see what happens" 😁

@mask477 12 жыл бұрын

Thanks GOD that he doesn't explain us on a black board or else the chalk factory would've ran out of COLORED chalks :D

@6bikal6 14 жыл бұрын

"I have infinite colors. I will never run out." I liked that

@Sweden8990 13 жыл бұрын

You really helped me. Thank you!

@Rayden440 12 жыл бұрын

wow it feels so good to understand things!

@Markolovrat 12 жыл бұрын

he has logarithm introduction video and 2 properties videos, this one is only about proving the properties

@agricolaterrae 14 жыл бұрын

I'm in AP calc, but I never actually understood this concept. Thanks for explaining!

@alexswift2k847 6 жыл бұрын

His handwriting got way better in the newer videos

@Danieltp3 15 жыл бұрын

great video man, very helpful

@R369B 12 жыл бұрын

Are there any, Intro to Log, Videos? Did I miss it, them somewhere? Thanks for the videos Sal. You've helped me find the fun in studying, that my past teachers K-12 were intent on watching die. So long as it suited them... Ya know the teachers are what is important. Keep up the Amazing Work. (Yes all you other "Teachers” out there WORK!) You rock man!

@lethinhchanhung 2 жыл бұрын

This video is a few months younger than me :))

@Brian626 16 жыл бұрын

wow i understood that... all i have to do now is to try and memorize the steps so i can understand more deeply

@JaPiCi 13 жыл бұрын

Thanks dude !

@amadoukoita 13 жыл бұрын

Excellente! I like it very much

@kadenmorash8054 11 жыл бұрын

Whoa, crazy coincidence. I'm doing a problem which is "Find the value of log(base 4) 256^3" 256^3=16,777,216.

@kishorkumarmishra9355 4 жыл бұрын

Thank you sir for such a nice explanation

@notmyrealnamr7190 7 жыл бұрын

"I have infinite colors, I will never run out!" lol

@FsMauri21 14 жыл бұрын

Thank you this was very nice :D

@Pritishammu 14 жыл бұрын

its too helpful

@cmcparland79 12 жыл бұрын

I wish you were my professor..why can't he just teach it like you do...it's sad that we pay hundreds of dollars for college courses and we have to go to KZfaq to learn :/ Great Job Sal :)

@amadoukoita 13 жыл бұрын

excellent

@SergeantNugget 11 жыл бұрын

I love saying logarithm over and over, logarithm logarithm logarithm logarithm logarithm logarithm logarithm

@roidroid 14 жыл бұрын

so it's just a logarithmic way of explaining one of the exponent rules: B^x * B^y = B^(x+y)

@hussainv1 13 жыл бұрын

lovely :)

@lazyperfectionist1 12 жыл бұрын

Sal, I've been working my way through the videos in the algebra section on the website, and they've been quite helpful, but when I get to this one, I'm completely lost. I've heard of logarithms before. I'm almost completely certain they have something to do with math. This is the extent of my understanding of them, so I rather strongly suspect I don't have the necessary background to follow this video. Where do I go to get it?

@FallenElite1017 11 жыл бұрын

"HELLOW." Me: o.o

@lalityt07 2 ай бұрын

I was born after 18 days when you post this video

@sirsagan 12 жыл бұрын

i think Sai Khan should be knighted.

@Nunes2000productions 11 жыл бұрын

HOLY FOCK!!!!

@cpm2021 6 жыл бұрын

Is the converse possible

@iwuvvparamore 11 жыл бұрын

This is just like a basic overview isn't it? I've gone through many situations where the power was unknown and I had to use Logs to solve it; especially application questions

@meroguney861 4 жыл бұрын

Thanks bro

@lisinka3 15 жыл бұрын

I thought that with RBG you can only get 16^6 = 16 777 216 colors, not infinite.

@prump1 12 жыл бұрын

im pretty sure that RGB and RBG is just opinion based. no one has ever stated that there is one specific way to say it. i mean its just red green blue. also his calculations were wrong. in a standard computer there are 255 shades of red green and blue, not 256. so there are 16 571 375 colors, not 16 777 216. maybe im just not counting zero but i dont know.

@amy8713 5 жыл бұрын

you just saved my grade

@JSSTyger 13 жыл бұрын

Perfect...I was looking for the proof. Great job.

@ruser0084 14 жыл бұрын

up^2*thumbs

@ruser0084 14 жыл бұрын

up^(2*thumbs) sorry 2*thumbs is the exponent.

@Helmutandmoshe 2 жыл бұрын

It's a bummer that these early videos are so sloppy looking and in such low resolution. Half the time I have a hard time reading it and have to go back to listen to what he says again. It would be great to take the time and re-do these videos since all of these series are becoming a long lived reference for students.

@Helmutandmoshe 2 жыл бұрын

@Just a guy who is an idiot Dude, I got me some glasses just like you said but they don't seem to make incorrectly formed letters transform their shape. Can you help me find some really great penmanship correcting lenses... dude?

@eddie01187 7 жыл бұрын

How do I calculate the value of log 14?

@amy8713 5 жыл бұрын

I'm a little late lol but if theres no base assume its log base 10 of 12 which equals 10^14 and then calculate that

@demiourgoslikes69 14 жыл бұрын

Sir, I wana say that, umm i don't know..lol....your great!!!!

@valdas0 13 жыл бұрын

Stumbling into properties is not the best way to understand them. And watching other guy doing it is worse. People need to see that there is a reason in doing every step you did and that you aren't just randomly writing whatever comes into your head and watch what comes out of it.