# What is LN?

Blahness
What is LN? (Example problem requested)

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

Last edited:

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

Gold Member
MHB
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.

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:
Werg22
Blahness said:
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. >_<

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:
Gold Member
MHB
Blahness said:
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. >_<

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.

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?

Homework Helper
Loren Booda said:
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: