Logarithms Part 1: Evaluation of Logs and Graphing Logarithmic Functions

[@ProfessorDaveExplains]

Whoops! At 0:50, I meant to show an exponential equation, like 2^x, instead of x^2, as 2^x is the proper inverse of log base 2 of x. Sorry!

[@ramayanishukla4365]

Happens

[@angelisvegan5826]

@Dhruv Chaturvedi exactly.. I'm confused.. totally confused

[@angelisvegan5826]

Help me professor.. I ain't getting that 2:51 point.. log base b of (y) = x should be the inverse function of y=b^x.. And look what you've written

[@randypreston9377]

you all prolly dont care but does any of you know a tool to log back into an Instagram account? I somehow forgot my login password. I love any assistance you can give me

[@samirmanuel8944]

@Randy Preston instablaster =)

[@enzoqueijao]

This is the point where mathematicians got tired of creating signs for their operations and just gave up

[@youtubeuserdan4017]

Imagine if addition looked like add(5,3)=8

[@fusion_42]

​@@youtubeuserdan4017👏

[@ivoryas1696]

enzoqueijao Eh, _close._

[@HAAH999]

You need to edit the video at 0:50, such that 2^x is the inverse of log_2(x) instead of x^2. However, this was an excellent explanation

[@ProfessorDaveExplains]

I can't edit videos once they're posted. I didn't specifically state that the functions are inverses, but I do see how what is shown is misleading. I pinned a comment so hopefully people will catch that!

[@Solicanz]

you are a genius, feynman level explaination, this concept finally clicked for me

[@Attalla-t9b]

For anyone who's confused about 2:51 (That he should've wrote log base b of (y) =x), he explained it in 2:21 (How the inverse was derived)

[@AriaHarmony]

Thank you for including graphing in your videos! The concept that all graphs can be seen as transformations of their most basic form is very important to me, it gives me a very good intuition on the equations and how they relate to their graphs. I have a question, at 2:57 that part always confuses me, why is it that b and x must always be positive? is -3^3 = -27 non-existent in the world of logs??

[@ProfessorDaveExplains]

It's a good question! It's simply that only for the set of positive bases can a function be continuous, so we just focus on what is mathematically useful.

[@AriaHarmony]

Oh I see! I didn't notice that something like -3^x wouldn't be continuous.. Thanks!

[@pinklady7184]

I am here, just revising my studies of logarithm. I hope you will make a playlist of logarithms.

[@Ereh729]

Taking precalc rn. You're a life saver.

[@MajedSalmaoun]

bro you are a legend i wish i knhow this channel before All Love For You

[@himanivachhani5575]

I love this thank you so much

[@diaverna]

Can you please make a video on Fluid Mechanics? 😭

[@basilrex4105]

Prof Dave's tutorial is as clear as a crystal. It is as if David is showing me how to overcome Goliath who is confronting me disguised as Math. Even anencephalous Maxine Waters will be able to understand the Prof.

[@enzoqueijao]

Thanks for sharing

[@jaineilsart1528]

Even dave the professor makes mistakes. He taught me more than math today.

[@nbthakar]

Great video and work, as always Prof. Dave!! Quick question for you. At the 0:51 mark, isn't the left side supposed to be 2 to the x, instead of x squared, log base 2 would correspond to 2 raised to so.e exponent?

[@ProfessorDaveExplains]

ah, technically yes! i guess it's ok because i was just speaking generally and i do the actual derivation properly later, but thanks for catching that!

[@angelisvegan5826]

Hey nishant!! A quick question for you too .. How on earth could x rest next to log base 2.. even when x is the exponent.. Cuz exponents aren't supposed to sit next to log base 2...that's the place for "result".... or am I missing something.. Like .. Log base 2 of 8 = 3.. And 8 is but result of 2^3.. but what they're doing is placing exponent in place of the "result"..

[@fernandoportal5422]

Thank you so much, i was struggling with this, but this video made it work

[@simonoraha]

Love your videos! Keep it up!

[@literallyfornobigreason9432]

Thanks king

[@Morfeucomvoce]

Good video!

[@ericard4165]

Is this video made by yourself? Awesome

[@ericard4165]

And what's the difference between root and log? Just expressing differently?

[@ProfessorDaveExplains]

totally different operations!

[@tGoldenPhoenix]

Done.

[@muskanmishra5581]

Kya baat hai sir!!! Bohot badhiyaa

[@rama-rao-y8u]

the translation is so inaccurate lol, this comment is actually praising

[@jaineilsart1528]

Mistake correction : square root of x squared is the absolute value of x. Time marker : 0:41

[@rachaelrathore3458]

For log x to the base 4 = 1/2, why isn't x = +-2?

[@ridmicmeena4123]

Same doubt

[@abhaypawar7433]

negative numbers arent continuous

[@gokucrafter9456]

I have a question, How do you solve (-2)^x=-8, I know the answer is 3 and know the workaround, but cannot solve it only using logarithm's definition.

[@humzahkhalid1886]

Is 2:52 right? Should y=b^x be logb(y)= x

[@insane7493]

yes it is f(x)=b^x then f of inverse of x is log base b of x he is just using y instead of function notation

[@centerfield6339]

This notation is absolutely insane. Instead of log2 16 = x, why not just write 2^x = 16?

[@ProfessorDaveExplains]

Logs are the inverse operations of exponents.

[@kbailkeri]

Yaaay i finished the comprehension in like 10 seconds

[@thatomofolo452]

Great 👍👍😃

[@SteelBB9]

I LOVE LOGSS

[@generaltheory560]

How can log be root over

[@felixzeng997]

hi dave i am confused about something you mentioned in 2:58, why couldnt the base be a negative number ? is anything wrong with log -3 （- 1/27）= -3 ? because -3 ^ -3 is - 1/27, isnt it ? or am i missing something ?

[@saveearth7907]

And as you know, unless we're getting into imaginary numbers, we can't deal with a negative number underneath a square root. ... So in summary, because we only allow the log's base to be a positive number not equal to 1, that means the argument of the logarithm can only be a positive number.

[@felixzeng997]

@@saveearth7907 many thanks

[@saveearth7907]

@@felixzeng997 no..thank you..

[@truesanatani2892]

@@saveearth7907 you know what.. there could be a problem like yours ..but the makers of logarithm did not allow log base or the argument to be negative..

[@Digitalbandits99]

@@truesanatani2892 @save earth are you both Twins♊!!

[@reasatprottoy7488]

4:00 why not -3?

[@primeprime1047]

You're right! We can say x=+/-3 too

[@jurilynperez111]

b must be positive and not equal to 1

[@angelisvegan5826]

How's that .. 2^x = log2x.. I mean... x wasn't supposed to be there.. Look at this.. 2^3= 8.. and we write it as log base 2 of 8 = 3.. I ain't getting it.. The problem is log base 2 of x.. x is the problem.. x should be outside the equal sign.....

[@Digitalbandits99]

Log2^x is not equal to 2^x....you are getting it wrong from here itself...

[@mattitoolu5051]

Always update me

[@littleretroship6403]

Oh I thought logarithms, exponents and roots were like a three way inverse operations

[@xxxhristopher]

Once again thank you Jesus of sciences. 🎉

[@slowfern]

2:22 can anyone explain please

[@slowfern]

nvm got it

[@aselim20.]

I watched it but I didn’t take notes.