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1 year ago in Mathematics , Theoretical Physics By Shabir Ahmed

Why is the logarithm with base e frequently used instead of base 10?

Textbooks often state that base *e* simplifies calculus, but I'm interested in the deeper mathematical rationale. Is this predominance a genuine, intrinsic property of the constant *e* itself, or is it more a convention that solidified because of its unparalleled utility in describing continuous phenomena?

high-frequency NaturalLogarithm Base-e

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By Robert Answered 1 year ago

This is an excellent question that gets to the heart of why some tools are fundamental. The privilege isn't arbitrary; it's an intrinsic property of exponential growth. The constant *e* is defined so that the rate of change of the function e^x is itself. Consequently, the derivative of ln(x) becomes 1/x, the simplest possible form. In practice, I've seen this elegance translate directly: when modeling any continuous process from population dynamics to quantum decay equations built on this base resolve with far less algebraic clutter. Base-10 is useful for scaling, but *e* is the language of nature's instantaneous rates.

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Why is the logarithm with base e frequently used instead of base 10?

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