Demystifying the Natural Logarithm (ln)

Hi Julien, I’m glad you found it useful!

The concept is so clear now! and the explanation is just awesome. Keep up the good work.

Thanks Jason!

This website makes sense of the things that even math teachers have to look up to do correctly.
Amazing job Kalid, absolutely amazing.

Wow, thanks for the kind words! I’m happy to be able to share my thoughts, I’m glad you enjoyed the site :).

[…] The natural log is not just an inverse function. It is about the amount of time things need to grow. […]

e^3 is 20.08. After 3 units of time, we end up with 20.08 more than we started with.

Should that read “we end up with 20.08 times what we started with?”

Whoops, that was unclear. Yep, it should be 20.08 times our initial amount. I’ll fix it up.

Very informative and helpful. I would appreciate it if you could explain how you would solve this problem.

Investor A invests $1000 at an interest rate of 5% compounded continuously and Investor B invests $500 at a rate of 8% compounded continuously. If both of them invest at the beginning of 2008, when will the value of their investments be equal ?

Can someone explain to me how e^(pi*i) = -1?

@Dave: Nice question. You basically want to solve this equation:

1000 * e^(.05 * t) = 500 * e^(.08 * t)

e^(.05*t) is how much growth the $1000 investment has after some amount of time, and similar for e^(.08 * t). If you take the natural log of both sides you can “cancel” the ‘e’ and solve for the amount of time needed.

@dasickis: Great topic, I’m planning on covering that eventually. First I’ll be writing about what complex numbers mean. I found a good explanation here:

This was a very informative site. It really cleared up all the bad blood between me and logarithms.

You know what? This site was just sooo good that I have to leave another comment. Thank you for this fabulous site.

sorry…it’s fabolous. Not fabulous

Thanks Brandon :slight_smile:

Cool is the word that comes to mind. Man and all these years I thought that these were some abstract concepts both ln and e. Thanks for letting us appreciate what they really are. I really keep looking forward to your new articles on math .I seriously suggest that you write a book on math and if you dont have the time then take some out of your schedule to write one :)…

Thanks Mohammad! There’s so much beauty in math, but it gets buried under lifeless proofs. People forget that these ideas emerged naturally, not by someone saying “Today I’ll define e as lim n->inf of (1+1/n)^n”.

I’ve been thinking about taking the top math/programming posts and putting them into a book… I think it’d be fun. Not quite enough yet, but soon :).

Thanks a lot! Before finding this site, I was trying to understand the meaning of ln and e on Wikipedia, and discovered the same circular logic that you mentioned. Keep up the good work! I look forward to future articles.

Thanks Thomas, glad you enjoyed it. I had that same run-around for a while myself.

Speaking of new articles, I just did a post on interest rates.

Wow - THANK YOU for putting this so simply!!! My friend used this term on the phone earlier. Since I had no clue what it meant, I went to Wikipedia and saw a horribly complicated, technical explanation -but you put it simply!! And true wisdom is being able to communicate a complex topic in simple terms. THANK YOU so much. You made my night!!