What is LN?

[Blahness]

Main Question or Discussion Point

What is LN? (Example problem requested)

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

 

[TD]

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

 

[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.

 

[Blahness]

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

Refresh his memory, please? x.x


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. >_<

 

[Werg22]

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

Refresh his memory, please? x.x


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. >_<

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

 

[Jameson]

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

Refresh his memory, please? x.x


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. >_<

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 [itex]\ln 27[/tex] in your calculator, it would tell you the exponent that if you took $e$ to that exponenet, it would equal 27.

 

[VikingF]

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

 

[Loren Booda]

TD,

Isn't that spelled "Naperian" logarithm?

 

[TD]

TD,

Isn't that spelled "Naperian" logarithm?

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:

 

[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.

 

[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.