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        1.WHY "e" IS SO SPECIAL?WHY ITS NATURAL?
2.WHY LOG BASE e CALLED NATURAL LOGARITHM?
WHATS SO NATURAL ABOUT IT?PLEASE REPLY.
8 years ago

Askiitians Expert Himanshu Geed - IIT Delhi
31 Points
										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) = ex 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. loge 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:
$\frac{d}{dx}\log_b(x) = \frac{\log_b(e)}{x} =\frac{1}{x\ln(b)}$
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.
Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best!!!Regards,Askiitians ExpertsHimanshu Geed

7 years ago
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