The binary logarithm 
is the logarithm to base 2.
The notation 
is sometimes used to denote this function in number theoretic literature. However,
because Russian and German literature use the symbol 
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 
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 
,
the units of information are obtained in bits. When 
is used instead, the units of information are known
as "nats."
