1.WHY e IS SO SPECIAL?WHY ITS NATURAL?

2.WHY LOG BASE e CALLED NATURAL LOGARITHM?

WHATS SO NATURAL ABOUT IT?PLEASE REPLY.

Dear Araku,

1. e is the unique real number such that the value of the derivative (slope of the tangent line) of the function f(x) = e^x at the point x = 0 is exactly 1. he number e is irrational; it is not a ratio of integers. Furthermore, it is transcendental; it is not a root of any non-zero polynomial with rational coefficients.

2. log_e is a "natural" log because it automatically springs from, and appears so often in, mathematics. For example, consider the problem of differentiating a logarithmic function:

If the base b equals e, then the derivative is simply 1/x, and at x = 1 this derivative equals 1. Another sense in which the base e logarithm is the most natural is that it can be defined quite easily in terms of a simple integral or Taylor series and this is not true of other logarithms.

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