The common logarithm is the logarithm to base 10. The notation
is used by physicists, engineers, and calculator keypads to denote the common logarithm.
However, mathematicians generally use the same symbol to mean the natural
logarithm ln,
. Worse still, in Russian literature the notation
is used to denote a base-10 logarithm, which conflicts with
the use of the symbol lg to indicate the logarithm to base
2. To avoid all ambiguity, it is best to explicitly specify
when the logarithm to base 10 is intended. In this
work,
,
is used for the natural
logarithm, and
is used for the logarithm to the base 2.
The situation is complicated even more by the fact that number theorists (e.g., Ivić 2003) commonly use the notation
to denote the nested
natural logarithm
.
The common logarithm is implemented in the Wolfram Language as Log[10,
x] and Log10[x].
Hardy and Wright (1979, p. 8) assert that the common logarithm has "no mathematical interest."
Common and natural logarithms can be expressed in terms of each other as
and
The common logarithm extended into the complex plane
is illustrated above.
See also
Lg,
Ln,
Logarithm,
Natural Logarithm
Explore with Wolfram|Alpha
References
Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon
Press, 1979.Ivić, A. "On a Problem of Erdős Involving
the Largest Prime Factor of
." 5 Nov 2003. http://arxiv.org/abs/math.NT/0311056.Referenced
on Wolfram|Alpha
Common Logarithm
Cite this as:
Weisstein, Eric W. "Common Logarithm."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CommonLogarithm.html
Subject classifications