What are natural logarithms used for?

Question

What are natural logarithms used for?

1 Answer

Impact of this question

2809 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-15T16:08:12

Hello,

There are lots of answers.

1) $ln$ is a function whose the derivative is $x mapsto 1/x$ on $]0,+oo[$ .

2) $ln$ has the property very useful : $\ln(x^y) = y\ln(x)$ . Now, you can solve the equation $3^x = 2$ by using $ln$ :
$3^x = 2 <=> ln(3^x) = ln(2) <=> x ln(3) = ln(2) <=> x = ln(2)/ln(3)$ .

3) In Chemical, you know the formula $[H_3O^+] = 10^{-pH}$ . Therefore, $ln([H_3O^+]) = -pH ln(10)$ , and
$pH = - ln([H_3O^+])/ln(10)$ .
Remark. $ln(x)/ln(10)$ is denoted $log(x)$ .

4) $ln$ is used for the Richter magnitude scale to quantify the earthquake.

5) $ln$ is used in decibel scale to quantify the noise.

...

Science

Math

Humanities

... and beyond

What are natural logarithms used for?

1 Answer

Related questions

Impact of this question