# The Symbol In

• Aug 2nd 2008, 06:31 AM
magentarita
The Symbol In
I am having trouble distinguishing between the symbol In and the word log.

(1) What's the difference between the two?

(2) What exactly does the symbol In mean?

• Aug 2nd 2008, 06:48 AM
Krizalid
It's actually $\displaystyle \ln,$ which means "natural logarithm."

The natural logarithm can be rewritten as $\displaystyle \log_e,$ where $\displaystyle e$ is a constant. In particular, most calculus books treat $\displaystyle \log$ equivalently as $\displaystyle \ln.$

($\displaystyle \log$ has the base 10, but there's no need to write it.)
• Aug 2nd 2008, 06:51 AM
Chop Suey
Log, unless otherwise specified, is usually considered to be base 10. Ln is simply a notation. Ln is actually log base e.

$\displaystyle \log{10} = \log_{10}{10} = 1$

$\displaystyle \log_e{e} = \ln{e} = 1$

Ln is an abbreviation for logarithmus naturalis. Read more here if you're interested:
Natural logarithm - Wikipedia, the free encyclopedia
• Aug 2nd 2008, 06:52 AM
wingless
Firstly, if you're talking about the logarithm, its ln (L and N) instead of In

1. ln is always the natural logarithm, (logarithm to the base e). But log can mean either the natural logarithm or logarithm to the 10.

2. ln means either logarithmus naturalis or logarithm napieren, I'm not sure about this.
• Aug 2nd 2008, 09:45 AM
CaptainBlack
Quote:

Originally Posted by Chop Suey
Log, unless otherwise specified, is usually considered to be base 10.

Only by secondary/high school teachers. To the rest of the world it is a logarithm to an unspecified base. (In computer programming languages it usualy denotes the natural logarithm)

If the base is important it should always be specified, or obvious from context.

RonL
• Aug 2nd 2008, 01:00 PM
magentarita
I learned A Lot Here
The replies here helped a lot. I finally got the notes that I missed in class.