Discussion

Logarithm to base of mathematical constant e, where e is an irrational and transcendental number approximately equal to 2.718281828459 is called

Answer: B

Base \( e \) gives the natural logarithm, written \( \ln x \) or \( \log_e x \), where

\[ e \;=\; \lim_{n \to \infty}\left(1 + \frac{1}{n}\right)^{n} \;\approx\; 2.718281828459 \]

It is called natural because it is the base at which the logarithm's own rate of change is simply \( 1/x \), with no stray constant:

\[ \frac{d}{dx}\ln x \;=\; \frac{1}{x} \]

Any other base introduces a factor of \( 1/\ln b \), which is why calculus uses this one throughout.

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