General Logarithm/Examples/Base Pi of Pi

Example of General Logarithm

The logarithm base $\pi$ of $\pi$ is:

$\log_\pi \pi = 1$


Proof

An instance of Logarithm to Own Base equals 1:

$\forall b \in \R_{>0}, b \ne 1: \log_b b = 1$

$\blacksquare$


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 $17$
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