is the notation used in physics and engineering to denote the logarithm to base e, also called the natural logarithm, i.e.,

The United States Department of Commerce recommends that the notation be used in this way to refer to the natural logarithm (Taylor 1995, p. 33).

Unfortunately, mathematicians in the United States commonly use the symbol to refer to the natural logarithm, as does TraditionalForm typesetting in Mathematica. The use of for different purposes by different mathematical communities causes considerable confusion, so extreme care is needed in determining if the symbol found in the wild refers to or .

The natural logarithm is implemented in Mathematica as Log[x], which is equivalent to Log[E, x].

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. http://physics.nist.gov/cuu/pdf/sp811.pdf.

CITE THIS AS:

Weisstein, Eric W. "Ln." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Ln.html