Logarithms Part 2: Base Ten Logs, Natural Logs, and the Change-Of-Base Property

We know about logs, so what are natural logs? Again, no, they're not made of wood. They are logs of base e! What is e? It's this crazy irrational number. Just watch this.

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[magellan]

This three installment series on logs and exponents is first rate and made me realize I didn’t understand them as well as I thought.

[python_parallax]

I dont know if u know or not but we can use logs in calculators with different bases.
This is how (For example log(2, 8)=3):
Press log button
Put your base the bracket, put a comma (press shift and the closing bracket button. Maybe diff from other calcs), Then type the other number and finally close the bracket.
But the change of base property still is a pretty handy trick

[codexcodexcodex]

In the calculator, I tried (log 8)/(log 2) and the answer is three. It really works.👍👍

[AlessandroZir]

you are a wonder of nature, man!!! 🙏🙌💓

[garretthilbig]

This math series has literally been carrying me for a while now. Hopefully it can carry me through Calculus next year though.

[Zone_Ranger]

A few of my calculators (Ti 84 plus CE, TI-Nspire, HP prime...) can do logs with any base I choose (b>0, b!=1)

[Jaydenzzz]

I can simply type in log(a, b) in my calculator, where a is the base and b is the result of a^x.

[SHMECCC]

I've never done these before and this lesson was fun. I'm happy to finally use the sandwich mode of my phone calculator

[horizonbrave]

So...just to clarify, it doesn't matter the magnitude of the interest, e will still be the same value? You could be proiding 2% interest, or 200% interest...the value of e, the rate at which the interest grows will forever be capped at 2.7183....etc?

[jogeshjoshi]

Very nice sir please Make a Video about Discovery of ( e - 2 . 7182 ) by Sir John Napier in the Year 1615 How it has been Invented Thanks

[comedygamer]

2:47 incorrect, e is rational because as you said... e-rational

[derex]

You didnt explain how to simplify the base with the value of the logs there is no video thus far on explaining it pls

[rajeshkumar-yvht]

dear dave 1/n means interest rate always 100% if it is 50% then .5/n, please reply it is correct or wrong

[mustafasaber]

Log 100/log 7
Log 30/log 5
ln 63/ln 8
ln 2.7/ln 3

[ryanhoyt]

Log 15 = 1.176

log 5 = 0.699

Can someone please tell me what is being done to convert them into decimals.

I know 1, 000 = 3

and I know I can type it into a calculator; but does anyone know what the calculator is doing to get these calculations.

For example 7 = 0.8451

It would be very much appreciated
Not knowing is killing me 😵

[girirajrdx]

Log 15 /log 5
Dont this becomes log 15 -. Log 5
Then
Log (15-5)=log 10?