Logarithms | Logarithms | Algebra II | Khan Academy

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Intro to logarithms. Learning that logarithms are just a way of expressing "the exponent that you have to raise a base to to get another number"
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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!
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[@christophermoore370]

This man is a saint. What a wonderful time we live in where a guy like Mr. Khan is kind enough to share his intellect and teaching ability on the miracle that is the internet so people like me can learn in 2 minutes what an entire expensive 3 hour college algebra lecture failed to do. Thank you, sir. It's people like you that make the world go 'round.

[@beautifulpain9794]

Christopher Moore true

[@lol-nd5it]

@@beautifulpain9794 they're just logarithms, it's not too hard

[@bhajjugade1546]

Christopher Moore your learning this in college lmao I’m in 8th grade

[@arthurmorgan4460]

@@bhajjugade1546 your cool.

[@harshbirbrar2830]

ur doing this in college, they're teaching me this crap in grade 11

[@JonLG490]

you were sent to this earth for a reason lol

[@LoveNoThotss]

dkm

[@skinach]

Because the purpose of his life is to... teach? Yeah Sal's a great teacher, but he's still a human with his own life...

[@Alphae21]

@@skinach its just a joke calm down

[@v06261]

@@skinach did you stretch before reaching that high?

[@RPDBY]

maaan, I always used to think about logarithms as of somethings mysterious and completely incomprehensible, but 2 minutes of this this video completely changed it

[@teoi]

lmao same

[@SuburbanExplorers]

lmao same

[@saifullahrahman]

thats it? thats all it is? i was afraid of this my whole life?

[@jenromeave4793]

HAHAHA

[@GermaphobeMusic]

"Let's learn a little bit about the wonderful world of logarithms" Sal sounds like he's on the verge of collapsing

[@elijahdeliztakis8718]

Not a native English speaker here. When I use Khan Academy I'm glad I spent all those hours learning English. It was worth it.

[@regret1484]

I got stuck on logarithm in high school, now my youngest son in 4th grade knows about it. I always had to just turn into the back of the book to find the logarithm, not understanding anything I was doing. Wow...simple and precise. Thanks Mr. Kahn.

[@lol-nd5it]

Logarithms in 4th grade? I'm doing them in college

[@NetBio-Senpai]

I am doing them during my neet preparation

[@spitfire8616]

@@NetBio-Senpai based, me too

[@avizoid3462]

@@lol-nd5it lol im doing them in 6th grade

[@yuvrajsharma3059]

*Khan

[@vivianz9133]

I’m failing algebra 2 😭 hopefully I can learn everything online bc I’m currently not able to learn anything in class.

[@StarexPlode]

Did you succeed?

[@thasthakir3125]

It's Been 13 years and Still Saving Lives...

[@wyatttomlinson3475]

These are fantastic review videos for studying for big tests! They're not just about learning, but re-learning as well. Now I'm getting more confident in my Honors Math 3 final tomorrow. Here we go! Why aren't these used everywhere in Math classrooms? They should be!

[@theskyesfall]

Is anyone else here from google classroom cus school is closed and they started online learning

[@ruthless_meh]

Me. I did 2 weeks of work under a day. I'm almost done

[@haziqridzwan5199]

Im here by my own and I got some words from other comments about khan academy.

[@politicallil7060]

I must say I'm here some 10 years later, and you have provided the best explanation for something I have not dealt with in 40-plus years. It's funny, but you learn a lot of math that you never come into contact with in your career or everyday life. However, this math course is a part of problem-solving for job training, so I need to learn it to pass it.

[@lanavest12]

I'm brazillian, and this class substitued any math class i had in my hole life. Congratulations, and sorry for any english mistake ☺

[@NNJAx]

Reviewing for college placement exams, really helped refresh my memory. thanks!

[@slimreaper9122]

Same for me right now lol

[@screaminginagony3601]

Thank you so much! I have my exam soon and our teacher hated every one of us and explained absolutely terribly. I didn't understand this chapter throughout the entire year and you've finally helped me understand it IN 7 MINUTES. Our teacher couldn't do it in a year!

[@blade913]

Thanks for the video! Needed a little refresher and this brought my previous knowledge back. Khan Academy is amazing, thanks for making so much of math simple and understandable.

[@chesssports7595]

I just wanna say thanks for putting out all of these videos. I'm studying Algebra 2 over the summer so I can take pre calc as a freshman, and you have been a great help, thanks!

[@CrazySaqMasterVideos]

I really do love this dude, learn so freaking much from him.

[@mattkessel36]

Had to review logarithms for chemistry. Completely left my mind from high school pre calc. Thanks!

[@sunny99chan]

I've been stuck when doing log for days until watching this detailed video :) Thx'a lot

[@halofifa]

You sir explained in 7 mins what my professor couldn't explain in 20. Thank you !

[@system128]

Had to skip a little bit [probably a unit or two] of Alg II because of a school change. This is very helpful!

[@woh7198]

i had testicular aids and my great uncle was diagnosed a coconut but after i saw this video, my jellybeans turned green

[@spectres4130]

Abraham Molina in english please

[@najjmx2422]

Abraham Molina yes

[@spectres4130]

@@NathanY0ung woah that was 11 months ago

[@valeroy3268]

Kumori whoah that was one year ago

[@amagicaltwinkie9126]

I’m currently learning geometry so I don’t understand why understand this so well wow khan is a legend

[@pkavenger9990]

In Simple words Log base 3 ( 81 ) means how many 3s do we need to multiply to get 81. I am learning Programming Algorithms and this subject will be essential when you learn about Binary search method.

[@shravyareddy506]

You are the best! Bless your soul

[@ludovicocalvetti1250]

Am I the only one who thinks Mr. Khan sounds like the Rock?

[@JonathanHernandez-ij2ht]

Yeah u are the only one

[@jade8144]

He's name is sal,and yes he sounds like Dwayne Jhonson

[@GuysCallMeShawna]

I needed a refresher. Thanks.

[@Hello-rg5bo]

SIR YOUR TEACHING IS AWESOME . AND YOUR EXPLANATION IS MARVELOUS

[@colincrenshaw9482]

I have a test tomorrow and my teacher is useless. This is a godsend

[@kokon3582]

thanks you so much. I am struggling with change of base

[@eonix493]

I`m 18, and I understand this (Only because your a SUPER-AWSOME TEACHER!!!!!!!!!!!) !!

[@patricksimmons8117]

you're. and this is very easy to understand

[@yukti4126]

I'm 14

[@TheHaakiiz]

so in that sense you think logarithms is easier than e.g. substiution? dumb

[@TrueLuizFalse]

I guess your language teacher wasn't?

[@ytpanda398]

@@TheHaakiiz I guess when you're past this stuff it's all pretty equivalent. At the time obv logs look a lot harder but they're not really. The graphs look terrifying until they're really not. In that sense they can be considered equivalently easy topics

[@glitterintheairxoxo]

These videos have made studying for the ACT so much easier. Thank you Sal!

[@twopolaar599]

Which country does the ACT? just curious

[@mathlogs605]

Great Khan sahab ... Will share with my students

[@jovannyvaldez3104]

I have a final in half an hour thanks to this I’m feeling more confident

[@Dule-my1yc]

This helped me so much!! Thank you kindly. :)

[@hendrinatweshy8458]

Thank you sir I'm doing my grade 11 you really helped me thought it was difficult

[@waleeeeeed21212]

One of the most important lessons you`ve ever made

[@byronjones3579]

such a great teacher

[@crpressler]

Will you be making a video that explains the natural log "e", or other uses of logarithms. Thank You for making this video.

[@alexaplaybtsbts463]

This is by far an AMAZING asmr!

[@muhayorahmatova8793]

Thank khan academy! I pass my test😊😊😊😊😊😊😊

[@Hello-rg5bo]

KHAN SIR IS AMAZING IN TEACHING

[@Dirty2D]

1 min into this and ive learned more than i ever did at school

[@200270258]

Holy Crap thank you so much, you're a really good teacher, and color coding it was very helpful, I couldn't undertand it cause my teacher made it sound so complicated. Thanks again, for sharing!

[@Ghost572]

Thats high school in general, i learned jack there because of the way they taught it. they just recycle the same shitty was to explain it on the way they taught it and if you don't get it then thats it you miss out. its nice now that we have plenty of options to learn.

[@Dundereshock]

I was interested in learning this after my teacher in alg 1 class used his calculator and it showed a bunch of logs... actually seems pretty simple

[@pokefan257]

I love pokemon too

[@CompleteRandomness22]

I'm sad that this was so simple. I really wish I had found this specific video when I was taking algebra in high school. I actually still couldn't remember logarithms (nor did I understand it at all). You made this very simple. My teacher was horrible the way she explained it and the way the class was taught was that we were put in groups. In high school, groups don't get ANYWHERE in learning. I hope I made sense lol

[@LoveHateSerendipity]

Your voice sounds like a story teller in this video. happy holidays Sal--

[@simplyella5794]

ahhh omg Tysm I’ve been kinda struggling with them!

[@nihal2997]

Thank you very much, God bless you ❤️

[@user-qn2dz3sw3t]

Awesome explanation

[@VIBEwithME_10]

So easy now thank you

[@aduryant5265]

Thanks Mr.Khan

[@ohh338]

not gonna lie, you got me on the last one.. great lesson.. I will say when you said, ok let's try another one, I was like NOOOOOOOOO:) I know you have to practice and take notes to get any subject.. math is no different.. thanks again!!

[@tomfrantz]

BEST teacher.

[@radin2053]

The best teaching video ever

[@jessicaamybrandt3219]

Thank you soo much 💕🙏🙏please do calculus with language

[@kuraibankusu]

Are we not gonna talk about how much this guy sounds like Chris Griffin? But seriously, thank you for this

[@contentart5169]

He is amazing

[@atticusmattionel]

Thank you sm for this

[@whattsy320]

you are the best!

[@maniruzzamansardar9630]

Amsome explanation 🎉

[@tingal]

Thank you! I got this as a sixth grader :D

[@GabrielLima-hp2lh]

Obrigado pelo video

[@leorhettgutsman5138]

Good job.

[@tankerwife2001]

THANK YOU

[@mariasalgado7061]

good video Mr khan I subscribed

[@followthepassion1530]

Thank you sir😊👍

[@user-ki4jc7il1n]

Thank you!

[@CSam-hc4uk]

Thanks a lot!

[@aikatasharma9431]

Sir what is the need of logarithms if we can use the basic notation to denote a no. As a power to other

[@zinger3max]

just to clear the last 2 statements: you can go on and on to infinity to see that f(x)=[x^x] ; while x->0, really approaches 1. therefore: 0^0=1.

[@EnesSahin1725]

I get overly energetic/enthusiastic early adulthood age Baltic/Slav man vibes from your voice.

[@ShamilAkhmadov]

Please tell me which program do you use to do all this stuff?

[@Baller-rb7on]

Khan Academy 10 years later teaching me more then my actual math teacher

[@kevinbeltran8118]

I'm in 8th grade and man there still teaching how to solve inequalities and equations Like damn they think we're stupid This is easy af and I'm sure teachers in my junior year (future) would take 5 months reviewing algebra 1 and the rest of the year doping around

[@emeraldralts]

You have to think about the average student. While you may be advanced in mathematics, you obviously aren't too enriched in English. Think of the average.

[@RejectReef]

Khan, you saint.

[@carlenger9707]

Thanks 500,000,000,000 times!

[@charitynalwimba4472]

Thank you

[@DarkBlockz]

this guy is the only reason why I haven't failed maths

[@ramentaco9179]

This should be in schools, god knows teachers can't explain it.

[@hollilyndora4518]

can someone please explain how 16 is the power? Other sites are saying the 4 would be the power--or the exponent, but nobody is assigning the power to the number in the 16's position. It makes no sense to me...but i admit I am struggling with this. This is from the intro to logarithms text page after the video. 24=16⟺log2(16)=4 Both equations describe the same relationship between the numbers 2, 4, and 16 where 2, is the base, 4 is the exponent, and 16 16 is the power.

[@philtrem]

It should read: 2⁴=16⟺log2(16)=4, which is correct. in 2⁴: 2 is the base and 4 is the exponent. In log2(16)=4: 2 is the base and 4 the exponent. You can notice a pattern in how a logarithm is represented: left: base, right: exponent, middle: base raised to the nth power (where n is the exponent)

[@darrencrissismyhero]

Hi! I love explaining why KZbin is educational to my friends. For my Government midterm, we are supposed to create a piece of legislation, and I have decided to do mine on education and technology. What do you think the U.S. government can do to link KZbin and Khan Academy, and the classroom?

[@SimplyaGameAholic]

ٌYou're amazing Sal you made it so simple !! :D

[@MatromJohn]

Solve for 𝑥 given the logarithmic equation 𝑙𝑜𝑔11(4𝑥 + 3) − 𝑙𝑜𝑔11(2𝑥 − 3) = 1

[@weareworkingonit]

Sal your a god.

[@xohlt1]

thanks

[@IBRAHIMSORIESESAY-uf5we]

you are the best math teacher ever you make me to understand log in math Tomorow we have math exam you have guide me a lot 💚💙💜🧡❤❤‍🩹

[@Charles-np4fn]

This is Better Than My Teacher Explaining.

[@MrAstroKind]

Because 10^1 = 10(*1) therefore 10^0 = 1 and 10^-1 = 1/10 notice you can multiply by 1 an infinite number of times and still get the answer. Also, there is a multiply difference between the numbers, conserving the logic (1/10*10^2= 10^0*10^1= 10^1*10^0 I hope that makes sense

[@mitsuru338]

Thanks

[@Male_Parent]

How do you solve them though?? Without a calculator

[@Zohirul-Jewel]

Watch the video, he shows you how.

[@eggizgud]

So, how does this apply in the real world? How is this knowledge used? Can someone explain? Thanks.

[@Someone-ig7we]

Grade 9 we have a question about finding what the exponent is and a couple asking the base if given the exponent and I research all this stuff about logarithms and she tells us we were just supposed to guess it... We weren't taught it so we were supposed to just trial and error, while I went and learnt how to find it using logs on a calculator... It hurts man...

[@computerinsects]

good

[@tomjeftabnd836]

thank so much you a good teacher

[@Drag0nzeyes]

Already starting to love this stuff. I had to briefly learn about this earlier in the year for my mathematics contest. My teacher was great, but I didn't quite understand the concept of logarithms within a short 10minute period.

[@MatromJohn]

Can you calculate this loga(2×+1) = 3^×

[@spliter88]

2^4 can also be seen as 1*2*2*2*2, 2^1 is 1*2, 2^0 is just 1