Fancier logarithm expressions | Logarithms | Algebra II | Khan Academy

Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacadem...
Examples of logarithms that evaluate to fractional and negative values.
Practice this lesson yourself on KhanAcademy.org right now:
www.khanacadem...
Watch the next lesson: www.khanacadem...
Missed the previous lesson?
www.khanacadem...
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: www.youtube.co...

[@rogerdotlee]

BLISTERING FARTBUCKET! After almost FIFTY YEARS I've found someone that can actually explain the difference between x^1/y vs x^-y without leaving me wondering if they were doing this just to taunt me! Thank you, Mr. Academy, for finally, after all these years, proving to me that Algebra was NOT designed to make me think that the world was out to make me look stupid. I've got a firm grasp on trig, my geometry is passable, and Calculus makes sense. But this is a first for Algebra. Thank you.

[@SarahTheAwesomeLaCroix]

Wow. That escalated quickly.

[@lars9310]

+Sarah «The Awesome» LaCroix Haha.

[@madblazer8401]

Hahahha :D

[@micosstar]

hehehe [:

[@jorgerivera6703]

You are better than my teacher

[@connorhowitt9164]

agreed

[@spongeycraftstudios4371]

same

[@rogerdotlee]

Indeed it is. My biggest problem was always involving powers, fractions of powers, powers of fractions, inverse powers of fractional inversions, and the meteorological inversions that hover over San Francisco all the time.

[@Gh0StSecurity]

dear mr.khan can u add more problems of integral calculus please? as diff. calculus? I love that problems :D make me feel so confident about my skills thank you

[@PurpleNoodles]

I feel so smart for understanding all of this xD

[@ampleman602]

IKR, I did the last one with complete ease, mine came in as 1/-3, but Mr Khan here wrote -1/3, I got scared for a second then my idiot self realised that its the same thing.

[@water6133]

@@ampleman602 lol

[@The_Noblesse]

Oh maaahh...goossshhhh..... I'm dyin

[@THE16THPHANTOM]

Weird, i like math more and more as time goes by, mostly because there is a lot stuff in my line of work that keep me coming to this channel and be amazed and say wow its that easy, after spending hours being useless to my colleagues.

[@BarunVishwakarma8888]

Sir ji great "I hope u understand "

[@shabbirahmeddar7765]

Kindly use brighter and bolder highlighter so that writin viewr may better see and comprehended the subject.

[@carlii435]

while listening all I'm hearing is Joe Swanson from family guy, hard to concentrate lol

[@projjalm]

I'm starting to enjoy these videos as much Sal does.

[@ironmaiden265]

you are awesome. I like the way you make it easy for us to understand.thanks a lot

[@mehreenayub6831]

What about the properties which allow you to conclude that log baseaxa=1 or common log10=1 or lne=1

[@julielemus55]

Dude you speak my truth ♥️

[@maalpajara4301]

nice!

[@purva_vj]

you are so damn awesome.... love your teaching... thnxx sir ;)

[@bigstuff52]

Khannnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn... great intuitive way to teach this...

[@yolandamiller1541]

can this be done in the TI-84 Plus calculator???

[@pointman6778]

Yes

[@omsrisairamtraders9]

Cool

[@toutankhamonskiller]

please make a video about the usefulness of logarithms

[@harshranjan5655]

1million view but only 1.2 k like. I can,t believe this.

[@jayasreepatil8960]

So understandable

[@Quizibo]

Hey Mr. Khan. Do some finance videos on Benjamin Graham and analyze his formulas.

[@byronjones3579]

your a great teacher yea I did enjoy this video loads amazing

[@environ.global]

How can I solve 2x log 5 + log 4 = log 8/25 - log 2 I found -2 as the answer

[@Seattle206723]

Thanks Sal, Been a while since Ive visited, but once again thank you.

[@luxfries1524]

How on has it been now

[@kimsssss]

What job are you at that uses algebra?

[@Seattle206723]

@@kimsssss I have a client that's has a older father that has . This this this and this wrong with his body. I have to supply a 2 RN's that will work 12 hr shifts 7 days a week. I have a demand of $50 hr for each + OT. How much do I charge my Client to cover all expenses and make a profit (X)? I use it all the time. In fact most people do and they just don't know it.

[@ibrahimhcaglayan]

Try making a graph of a parameter whose values vary between 100,000 and 0.0001! That is when you need logarithms. Also, you hear in logarithms, you smell in logarithms, your hair and fingernails grow in logarithms, etc etc... Life is based on logarithms!

[@lamo867]

I understand just about everything in this video, except for the equations that inquired the negative variable, which is basically half of the lesson... (*Face Palm*) None the less, I still learned something from this lesson, and I greatly appreciate the teachings. I go to what some may call a, "special school", and the teachers think I basically am retarded so they won't let me even try to grasp the more difficult levels of math, such as Calculus... :c #TheStruggleIsReal ...

[@lars9310]

+lamo867 haha. dont let anyone tell you that you're dumb. I think the majority of our potential IQ lies in dedication and mindset, not how fast we can learn. :-)

[@heinthantsin4330]

I have a test tommorow thanks

[@EngineeringRevised]

Big-O Complexity is one great example of usage

[@lexiesmiski]

THANK YOU SO MUCH

[@davids1700]

I enjoy all your explanation. Very good!!! Do u explain Primitives also 4 instance?

[@KingTv.]

I don't think he is going to answer you.

[@robertpotapenko2648]

@@KingTv. me too

[@dlynn101]

I'm, having a devil of a time finding examples of problems such as "log base 1.5 of 2.3"

[@supdenfoosukka]

integrals of 1 over a function to the -1

[@jimverdalupan9510]

ow

[@ufufu001]

confusing as fuck

[@TheRafelito19]

is there somthing more advanced ? for expample dealing with ln and E

[@qwaszxerdfcvvcfdrexzsawq3470]

Rafael Santana if you go to actual Kahn academy then they have a few programs there on e and ln

[@oyudie2745]

Its not actually more complicated its just e is always the base

[@LeetCodeSimplified]

1.1 million views, only 89 comments? My guess, a lot of people must be watching this outside of youtube, embedded.

[@absarachowdhury7441]

How do u do this sum? 1+2lg x =lg(11x-3)

[@lukemavericknilo3228]

what if the base and its exponent has the same number how can you solve that??

[@firebloom02]

If you have a logarithm that looks like this: log(base2)2, the answer to this problem would be 1. If the base and its exponent and the exponent are the same exact number, the answer should always be 1

[@raanoooshh9296]

@@firebloom02 correct

[@methasawijayasuriya6472]

Sal why is the mantissa positive always?!

[@stav200139]

you so smart

[@bodrulahmed858]

Salman Amin Khan now I know you are Bangladeshi. we are proud of you !

[@alonsopereyra8482]

If someone could help me that would be great: X^-1/3=1/2

[@vishaljain4915]

i think you have the answer by now but anyway: x^-1/3 = 1/x^1/3 which is basically 1/cube root of x now we know 1 / cbrt(x) = 1 / 2 we can flip both sides by cross multiplying and get cbrt of x = 2 then to get x we just cube both sides to get ride of the cube root on x and we end up with x = 2^3 which is 8.

[@M4rtingale]

It's time for some Yule log!

[@chrisarrow]

1:25 but why?

[@Threetri333]

Why didn't I have these videos 11-12 years ago?

[@tamaht.7581]

My brain is trying to make sense of this 😓

[@PotatoBoiOfficial]

4:20 noice

[@raviaditya9142]

Anyone in 2019

[@deadprofile5983]

i have a question why 1/3? Explain why someone plz.

[@nilskiisler3032]

+Giovanni Fuentes I can't understand that neither, 8`1/3 is 2/2/3. Or am i calculating something wrong.

[@racheldellegatto7382]

8 is a larger number than 2, so you would have to use a fraction in order to find the x of 8. If this were the other way around and we were trying to find the x of 2, it would be 3 because 2•2•2= 8. So the answer would be 2^3=8. But as I said, since 8 is bigger than 2, it would be 8^1/3=2.

[@YongkangJR]

+Rachel Dellegatto but 8^1/3=2/2/3, not 2, 8^1/4 is 2 though, did he mean to write power 1/4 instead?

[@YongkangJR]

+Yong Kang I found an answer to a question similar to mine on the khan academy website: "Incorrect. There is a difference between ^ and *. You are thinking of 8*1/4, which is 2. The ^ indicates the exponent. This uses multiplication, but is not multiplication. Normally you're used to seeing ^2, or squared. This would mean you repeat the number 2 times and then multiply, so 8*8 = 64. Does this only works when you see the whole numbers? NO! The fraction 1/2 is the inverse of 2 (or 2/1). Therefore the operation is the inverse, so instead of squared, we need square root. For example 9^1/2= 3. Now for the 1/3. If it was 3/1, you would say cubed. Therefore since we have the inverse fraction, we instead need the cubed root. This means what number multiplied by itself 3 times results in the number 8? This answer is 2. 2*2*2=4*2=8. Therefore 8^1/3=2." But i still don't get it, what is the difference between ^ and *?

[@094s9]

log8 of 2 = x. 8^x = 2. Change the bases so that they are equal. 8 = 2^3 2^3x = 2^1 Solve for x. 3x= 1 Divide both sides by 3 to isolate x. x= 1/3.

[@blake1662]

Nice vid - first viewer first comment

[@flowinori00]

Too fast bruh😂

[@PhrozenTiger]

Now.. take log(2) of -8 ... >=)

[@michaeltao81]

I don't get this??

[@intellexual9097]

Thanks for the lesson! -cue Iggy Azalea's song "Fancy"-

[@johnsongeorge3268]

I aint enjoyed 4:15 ;)

[@mikel1888]

0-100, REAL QUICK

[@IshanTheAwesome]

Negative logs can't be calculated!

[@deadprofile5983]

nvm

[@charity4613]

public education sucks

[@karensanchez4708]

i understand a lot better but his voice madd anoying bruh.

[@Carlisle412]

I think it was meant as a joke.

[@jsf3669]

bruhhh... "Fancier"..............

[@ewerybody]

1:23 eeeeeekk! Wait a minute! "Well if 2 to the 3rd power is 8. 8 to the 1/3rd power is 2!" Why is that so?! Probably I need to see stuff about exponents? Because for me that aint obvious! 😐

[@chaaruruuu4587]

yea you need to understand exponents bc logarithms are kinda like the inverse or reverse of exponents or exponential equations

[@oyudie2745]

Its like your going backwards like imagine if the 1/3 dosen't exist and look at only the 3 now what number to the power of 3 = 8 well that would be 2

[@vevenaneathna]

thats the joke...

[@dramaqueen9475]

this video was SO not helpful. u didnt tell us how to solve anything. all u did was get straigh to the answer with any problem solving.

[@ibitoyetoyin6018]

He didn’t solve them because he had solved several similar examples in the videos before this.

[@reinaldodepedro]

To understand this video, try learning first properties of exponents, then with negative fractional exponents. Second try learning properties of roots, then learn square and cubic roots. Third learn properties of logarithms. Success.

[@Jazoopi]

thats how logs work

[@ryanperez8179]

For all have sinned, and come short of the glory of God; Romans 3:23 Jesus lives Jesus Christ is Lord Jesus loves you repent You're a sinner in need of a Savior