Binary logarithm

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In mathematics, the binary logarithm (log2 n) is the power to which the number 2 must be raised to obtain the value n. That is, for any real number x, x = log 2 ⁡ n ⟺ 2 x = n . {\displaystyle x=\log _{2}n\quad \Longleftrightarrow \quad 2^{x}=n.} For example, the binary logarithm of 1 is 0, the binary logarithm of 2 is 1, the binary logarithm of 4 is 2, and the binary logarithm of 32 is 5. The binary logarithm is the logarithm to the base 2 and is the inverse function of the power of two function. There are several alternatives to the log2 notation for the binary logarithm; see the Notation section below. Historically, the first application of binary logarithms was in music theory, by Leonhard Euler: the binary logarithm of a frequency ratio of two musical...

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