Natural Logarithm of e is 1

Theorem

$\ln e = 1$

where $\ln$ is the natural logarithm, $e$ is Euler's number, and $1$ is the identity element of multiplication.

Proof

The definition of the Euler's number as the Base of Logarithm will be used.

Then the result follows directly.

$\blacksquare$

Also see

• Equivalence of Definitions of Euler's Number for other definitions of Euler's number

Sources

• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.2$: Numbers, Powers, and Logarithms: Exercise $17$