Logarithms - e - Euler's Number

This math video tutorial provides a basic introduction into the number e, it's relation to logarithms, and how e - also known as euler's number - is calculated.

Log to Exponential Form:

Change of Base Formula:

Change of Base Log Problem:

Properties of Logarithms:

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Expanding Logarithmic Expressions:

Condensing Logarithmic Expressions:

Natural Logarithms:

Solving Exponential Equations:

Exponential Equations - Quadratic Form:

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Solving Logarithmic Equations:

Graphing Logarithmic Functions:

Graphing Exponential Functions:

Compound Interest Word Problems:

Logarithms Practice Problems:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

Logarithmic Formula Sheet:

[josephrichards]

How does this guy know so much lol, so many topics I look up and he has a video on it explaining it easily. I have to say, you are doing a fantastic job and are clearly a very smart guy. Props!

[cluskyhardway]

Sir, I owe you a lot.. Imagine an anglophone schooling in a francophone country... If not for your lessons life wouldn't be easy at all

[pingpong]

You are the reason why I am doing amazing in grade 12 math.

[laurenorourke]

I'm learning about logarithms in algebra 2 right now and this is really helpful and helps me get a really good insight on what e means. Thank you so much!

[georgesadler]

MR. Organic Chemistry Tutor, thank for a basic introduction to Euler number e and its overall application to growth/rate in real life. The number e is well known in pure and applied mathematics.

[popeye]

Where does "e" come from: It from a space right between "D" and "F" remember... Now that I solved that mystery, I still need to find my remote.

[georgettebeulah]

This is so true I can understand a lot from it, rates and euler formula make so much sense and meaning, I get it thank a lot. Love you much.

[Innotutorial]

He inspired me to create quality tutorials

[vikramnagarjuna]

Hi sir, This is vikram from India,
I need this type of Mathematical tricks. Do video on zero factorial by using advanced Mathematical methods.

[hiel]

At 1:21, where does the term “1” come from? As in “A = P (1…”. What does the 1 represent in reality? Why is it there?

[SiEmG]

can someone explain to me:

1. In all videos related to Euler's number, they all start with this example of 100% growth/rate over some time (e.g. 1 year) and then split the rate/growth to 50% and 50%. What is the logic of this? When you say 100% interest to your x amount in 1 year, you do not mean x+ (50%*x) + ( x+ (50%*x)) *50%. This is not a 100% rate anymore but a more complicated higher rate. wtf? For me, it is not something I can relate to something I know. How should I think of it?

2. Also how this can be used on a simple example e.g. with some initial population of microbes and an arbitrary infinitely constant growth rate (e.g. 250% or 50%), an arbitrary initial and final population (e.g. 101 -> 10101 units), and an arbitrary time period (e.g. 4000 days)?

[brendhalarys]

But how does the first explanation for e work with numbers bigger than 1?

[niceguy]

But how exactly did we get the value of e
If all the proofs that is shown in the vid is said to be closer and closer to e?
How did we get the exact value of e at the first place?

[randomvidson]

Still searching for videos on vectors and mechanics and dynamics as well

[samiulislamdurjoy]

G 194
note: 9:54 the slope and area of e^x is same as y

[FizzyToni]

When u say 100% interest twice a year or four times a year u mean 50% interest twice a year, 25% interest four times a year, right? Since if you got 100% interest twice a year starting with 1$, you would have 4$ after the first year

[boqorkhan]

Sir I want to talk about next indices.

[theophonchana]

#logarithm #log #e #euler #eulernumber

[jasminepreen]

Math?! MATH?!

*Maths. There! You have been corrected. 🙂

[digitalwizgraffixinc]

Can anyone solve these Do these for me?