Logarithms
Natural logarithms
None
Calculator for natural logarithms
Calculator for Natural Logarithms
Discussion and questions for this video
Do you understand English? Click here to see more discussion happening on Khan Academy's English site.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

Have something that's not a question about this content? 
This discussion area is not meant for answering homework questions.
ln = logarithmus naturali Latin not French.
In french, ln = logarithme népérien, which translates to "Néper's logarithm'. Néper is a frenchization of Napier, as in john Napier (http://en.wikipedia.org/wiki/John_Napier), who invented logarithms.
ln = logarithmus naturaliS
That's not a question. Post that in the Tips and Thanks column instead next time.
Why are ln and e so important?
Invest $1.00 at 100% interest for 1 year.
Compound:
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.
Compound:
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.
Sal said in the last video that e occurs so much in nature
Are there any videos are playlists specifically covering "e"?
Thanks Marty! I looked and I found http://www.khanacademy.org/math/precalculus/v/introductiontocompoundinterestande in case anyone else is looking.
I think that there are some in the precalculas playlist, but I haven't seen any myself.
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.
you could try looking for videos of halflifes and stuff because they use natural logs
hope this helps :)
hope this helps :)
why is ln (1) undefined??
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
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
Actually it stands for "logarithme neperien" in frensh
At 0:45,what is mantisa
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.
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.
how do i use the calculator for e to the 0.24?
press the e button
press the ^ button
type in .24
press =
press the ^ button
type in .24
press =
or you can find a button labelled e^x. push 0.24 and hit the e^x.
how do you find "ln" on a TI84 plus calculator? if you can't, then how would you start to solve the problem 2e^2ln4  ln e^8 ?
it's the button directly on the left of 4
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 computerinputed 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:
10000
times
(
(
10
÷
17 (10/17)
)
ln(x) (natural log of 10/17)
)
= (10000 times the natural log of 10/17)
÷
80
=
10000
times
(
(
10
÷
17 (10/17)
)
ln(x) (natural log of 10/17)
)
= (10000 times the natural log of 10/17)
÷
80
=
Im having trouble figuring out how to use my calculator (TI30XA) to answer x= In(3/5)1 / 2
The answer is .755 but I dont know how to get there.
The answer is .755 but I dont know how to get there.
how do I use calculator to logarithm function division problems
Could we please have some videos explaining more about what e is, where it came from, and how it's useful? Thanks!!
Try watching sal's vids on "compound interest and e"
so is there a section for natural logs like this: 1+LN(x)2=6 (one plus natural log x squared equals six)
To solve that I would start by subtracting 1 from both sides.
how to check answers using a log table?
how to change the base of log from "e " to base 10
C=2pier solve for r
Why is ln(0) undefined?
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.
Find the interest of $23,400 at 14.5% for 24 months
what is the best way to deal with natural logarithm word problems?
any thing in particular i might want to look for?
even nonnatural logarithms, what's a real life senario where they might apear?
any thing in particular i might want to look for?
even nonnatural logarithms, what's a real life senario where they might apear?
How do you deal with logarithms when placed in word problem form, or real life?
ok im confused!
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.
http://en.wikipedia.org/wiki/E_(mathematical_constant)#Compound_interest
One example where e occurs naturally is the capstan equation.
http://en.wikipedia.org/wiki/Capstan_equation
http://en.wikipedia.org/wiki/E_(mathematical_constant)#Compound_interest
One example where e occurs naturally is the capstan equation.
http://en.wikipedia.org/wiki/Capstan_equation
2log6(x+9)=log6(36+2)
Discuss the site
For general discussions about Khan Academy, click here.
Flag inappropriate posts
Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians.
abuse
 disrespectful or offensive
 an advertisement
not helpful
 low quality
 not about the video topic
 soliciting votes or seeking badges
 a homework question
 a duplicate answer
 repeatedly making the same post
wrong category
 a tip or thanks in Questions
 a question in Tips & Thanks
 an answer that should be its own question
about the site
 a question about Khan Academy
 a post about badges
 a technical problem with the site
 a request for features
Your SpinOffs
Share a tip
Thank the author
Have something that's not a tip or thanks about this content?
This discussion area is not meant for answering homework questions.