Binary Logarithm/Examples/32

Example of Binary Logarithm

The binary logarithm of $32$ is:

$\lg 32 = 5$


Proof

\(\ds 2^5\) \(=\) \(\ds 32\)
\(\ds \leadsto \ \ \) \(\ds \lg 32\) \(=\) \(\ds \log_2 2^5\)
\(\ds \) \(=\) \(\ds 5 \log_2 2\)
\(\ds \) \(=\) \(\ds 5\)

$\blacksquare$


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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