Binary Logarithm

The binary logarithm log_2x is the logarithm to base 2.

The notation lgx is sometimes used to denote this function in number theoretic literature. However, because Russian and German literature use the symbol lgx to denote the base-10 logarithm and since this is the use recommended by the United States Department of Commerce (Taylor 1995, p. 33), this practice is discouraged. (To confuse matters even more, some German literature uses the notation ldx to mean the binary logarithm.)

The binary logarithm is implemented in the Wolfram Language as Log[2, z] and Log2[z].

When information theoretic functions (like entropy) are computed using log_2x, the units of information are obtained in bits. When log_ex=lnx is used instead, the units of information are known as "nats."

See also

Common Logarithm, Lb, Lg, Logarithm, Natural Logarithm

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Taylor, B. N. Guide for the Use of the International System of Units (SI). United States Department of Commerce. NIST Special Publication 811, p. 33, 1995.

Referenced on Wolfram|Alpha

Binary Logarithm

Cite this as:

Weisstein, Eric W. "Binary Logarithm." From MathWorld--A Wolfram Web Resource.

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