# What is LN?

1. Sep 22, 2005

### Blahness

What is LN? (Example problem requested)

What is LN in math, and how do you solve the LN of something?

Last edited: Sep 22, 2005
2. Sep 22, 2005

### TD

The "ln", nowadays also just denoted as "log" is the natural (or neperian) logarithm, meaning the one with base e (2.718...)

3. Sep 22, 2005

### Jameson

ln is called the natural logarithm in math. It is a logarithm with a base of $e$

$$\ln{x}=\log_{e}x$$

We use ln as shorthand notation but the above notation is equally correct.

To take to natural log of some number, let's call it A, is to find another number, let's call it B, so the $$e^B=A$$

Hope that gets you started.

4. Sep 22, 2005

### Blahness

Erhm... My friend doesn't know what a logarithm is.

EDIT: Durr, posted while I typed. Thanks! Y.Y

Lemme make sure I have this clarified.

Let's make A = 27 and B = 3.
(can't use latex here)

Loga = B
Log(27) = 3
E^3=27
E = 3

Is this right, or am I confused?

Give me an example problem, step by step, please. >_<

Last edited: Sep 22, 2005
5. Sep 22, 2005

### Werg22

Logarithm is the inverse of power. Logorithm goe as such:

10^logx_base 10=x

Exempe:

10^x_base10=100
10^x_base10=10^2

x_base10=2.

ln is base with base e. If you are wondering what is e, if you integrate the area of the function y=1/x between x=1 and x=a, the only solution for a that gives an area of 1 unit is e.

We write log_baseex simply as lnx.

An exemple is;

5^x=4

You can solve this with logs;

(10^log5)^x=10^log4

10^(xlog5)=10^log4

xlog5=log4
x=log4/log5

The basic relationships

a=log(xy)
a=log((10^logx)(10^logy)
a=log(10^logx + logy)

Since we know that

10^log(xy)=10^logx + logy,

then

log(xy)=logx + logy

Last edited: Sep 22, 2005
6. Sep 22, 2005

### Jameson

Sorry, this is incorrect. $e$ is a constant. It is defined as $$\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^{x}$$ and is around 2.71.

You won't be able to calculate numbers such as $\ln 5$ or $\ln 1000$ by hand. I'll use your numbers as an example.

$$\ln x = \log_{e}x$$

So let's say that $$\log_{e}A=B$$

that means that $$e^B=A$$

You said A was 27 in your previous post. If you typed in $\ln 27[/tex] in your calculator, it would tell you the exponent that if you took [itex]e$ to that exponenet, it would equal 27.

7. Sep 22, 2005

### VikingF

ln(a) is the area under the graph y=1/x limited by the lines x=1 and x=a.

8. Sep 22, 2005

### Loren Booda

TD,

Isn't that spelled "Naperian" logarithm?

9. Sep 23, 2005

### TD

That's quite possible, I tried translating it from my language
Both get google hits but yours a bit more, so it's probably "Naperian" :tongue2:

10. Sep 23, 2005

### HallsofIvy

"Naperian" (notice that both Loren Booda and I are capitalizing it) is named for John Napier (apparently the "i" got lost somewhere), a Scottish mathematician- you don't "translate" people's names! Napier also, by the way, invented the decimal point.

11. Sep 23, 2005

### TD

In Dutch, it's called the 'Neperiaanse' or 'Neperse' logarithm, and I tried to "translate" that into English. I'm aware of the fact that it comes from a person, but that doesn't change the fact that the term is different in multiple languages.
Of course, his name is the same everywhere, but the term for the logarithm (which was derived from his name) can be different in other languages.

Last edited: Sep 23, 2005