Calculator for natural logarithms

Calculator for Natural Logarithms

Calculator for natural logarithms

Discussion and questions for this video
Invest $1.00 at 100% interest for 1 year.

Quarterly: $2.44
Monthly: $2.61
100 times: $2.70
1,000 times: $2.72
10,000 times: $2.72
100,000 times: $2.72
1,000,000 times: $2.72

You eventually compound that one dollar so much annually that this is called "compounding continuously".
The value is approaching a limit called "e".

That's why e is so important. To compound continuously.

Hope that answered your question.
okay so, on the topic of natural logs, could there be some videos where the application of natural logs is necessary?
I think logs and natural logs are also used for continuously compounded interest rates banks use for your bank accounts. I don't want to be a parrot, but from an in class lecture my professor gave a little backstory about Euler, banks using it as some scheme to lure customers away from competing banks, and to help give some explanation behind certain measurements naturally occuring in plants.
Good Question!
It's the same as saying 'e' to what power equals negative one
e^x = -1
There is no real number for x that makes that equation true
The mantissa of a logarithm is the decimal portion of the answer. We usually speak of the mantissa when dealing with the common log rather than the natural log.

For example, log₁₀ (152) = 2.18184 (rounded off)
The mantissa is 0.18184...
The characteristic (which is the integer portion of the answer) is 2.

This is mostly just a curiosity nowadays, since calculators and computers have made needing to separate the characteristic and the mantissa obsolete.
The natural log and the exponential function with a base of e are inverse functions. Thus, the cancel each other out. Therefore.
`e^(ln x) = x` and `ln(e^x) = x`
Thus, in your example the answer is `-3`
If you get a question that says round to the nearest hundredth (for example) and you got a number like 1.1, would you have to put the extra zero at the end, or could you just keep it as 1.1 since the final zero is not needed?
It is an issue of significant figures. If the numbers you are given have that accuracy, then there is a point to adding the zeros, additionally for computer-inputed answers. For paper grading without significant figure requirements it should not matter.
I am having trouble finding the correct answer on a calculator for P(t)=10000e^ln10/17 over 8 times 10? I'm not sure how to enter it. I have been playing around with examples and I am not coming up with the correct answer. Please help.
I'm not sure if you mean (e^ln10)/17 or e^ln(10/17), but either way it works out the same. The natural log is defined as what power you need to raise e to to get a number, so e^ln of something is just that something. So we have 10,000*10/(17*8*10) = 10,000/(17*8) = 1,250/17. On a calculator, you would press the buttons like this:
17 (10/17)
ln(x) (natural log of 10/17)
= (10000 times the natural log of 10/17)
Im having trouble figuring out how to use my calculator (TI-30XA) to answer x= In(3/5)-1 / 2

The answer is .755 but I dont know how to get there.
Could we please have some videos explaining more about what e is, where it came from, and how it's useful? Thanks!!
so is there a section for natural logs like this: 1+LN(x)2=6 (one plus natural log x squared equals six)
For the same reason that log(0) is undefined for any other base. For b ≠ 0, there is no x such that b^x = 0.
what is the best way to deal with natural logarithm word problems?
any thing in particular i might want to look for?
even non-natural logarithms, what's a real life senario where they might apear?
I'm just wondering, but how does "e" show up in nature and finances?
There is a connection to compound interest frequency, thats how the constant was discovered.

One example where e occurs naturally is the capstan equation.