Floor Function/Examples/Floor of Binary Logarithm of 35

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Theorem

$\floor {\lg 35} = 5$

where:

$\lg x$ denotes the binary logarithm ($\log_2$) of $x$
$\floor x$ denotes the floor of $x$.


Proof

\(\ds \lg 32\) \(\le\) \(\, \ds \lg 35 \, \) \(\, \ds < \, \) \(\ds \lg 64\)
\(\ds \leadsto \ \ \) \(\ds 5\) \(\le\) \(\, \ds \lg 35 \, \) \(\, \ds < \, \) \(\ds 6\)

Hence $5$ is the floor of $\lg 35$ by definition.

$\blacksquare$


Sources