1.WHY LOG TO THE BASE "e" IS TAKEN IN PHYSICS?WHY NOT pi OR ANY REAL NUMBER?

2.WHY "e" IS SO SPECIAL?WHY ITS NATURAL?

3.WHY LOG BASE e CALLED NATURAL LOGARITHM?

araku valley, 14 years ago

Grade:11

1 Answers

Ramesh V

70 Points

14 years ago

The function e^x so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base e.

The number e is of eminent importance in mathematics/physics, alongside 0, 1, π and i. Besides being abstract objects, all five of these numbers play important and recurring roles across mathematics/physics, and all five constants appearing in one formulation of Euler's identity.

The number e is also called Euler's number.The number e is irrational; it is not a ratio of integers.

The numerical value of : e = 2.71828 18284 59045 23536….

In Physics: Natural processes like growth or decay (number of atoms, size of population) are functions of e to a given power.

natural logarithms are logs to the base of e.

what makes e so special that it just seems "natural" to use it as the basis for logarithms.
So I'll attempt to say it clearly.

Suppose you had a function f(x) that had this characteristic:
If you make a graph of f(x) and then check the slope of the graph at various points, you discover that the slope is always equal to the value of f(x)!
If f(x) = 1, then the slope at that point is 1. If you try a different value of x, and find that f(x) = 2, then the slope at that point is 2.
If there is a point where f(x) = 0.1, then the slope at that point is 0.1. Or if f(x) = 0, the slope is 0.
And if at any point f(x) = infinity, then the slope is infinite.

It turns out that there is a function with those characteristics, and it is an exponential function (like 10^x or 2^x). The particular function that has this characteristic is f(x) = e^x, where e has been found to be a value of approximately 2.718281828....

P.S: I thin its a long explanation, but for IIT these all things r not required ...i think u understood wat i'mtrying 2 say Mr. Araku

regards

Ramesh