Logarithms Part 1: Evaluation of Logs and Graphing Logarithmic Functions

What are logs? No not like the ones from trees, silly! We need to know about logarithms. They represent the inverse operation of exponentiation. How do they work? How do we evaluate them? How do we graph them? Let's go through the basics now.

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[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!

[enzoqueijao]

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

[Solicanz]

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

[HAAH]

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

[Attalla-tb]

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??

[pinklady]

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

[MajedSalmaoun]

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

[diaverna]

Can you please make a video on Fluid Mechanics? 😭

[Ereh]

Taking precalc rn. You're a life saver.

[basilrex]

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.

[ericard]

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

[jaineilsart]

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

[jaineilsart]

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?

[fernandoportal]

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

[gokucrafter]

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.

[rachaelrathore]

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

[humzahkhalid]

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

[ericard]

Is this video made by yourself? Awesome