whereby

which means "x is equal to 2 to the power of y". The equation can be turned around and reexpressed in logarithms as: [3]

Properties

Logarithms have the useful property that when numbers are multiplied, there logarithms are added:

Likewise, when numbers are divided, their logarithms are subtracted from one another:

Common logarithms

If the base is 10, the logarithms are called "

which has common usage in many applications in science and engineering.

Natural logarithms

If the base is e (where e = 2.71828 ...) the logarithms are called either "

or

which are taken to be equivalent notation formats. The natural logarithm has widespread in pure mathematics, especially calculus.

Notation confusion

The natural logarithm, to note, may often tend to be written with the base e "assumed" simply as:

This implied e base assumption, however, often times may become confused, often among chemists and engineers, as being a common logarithm, base 10 assumed. Chemists, for example, frequently use the symbol log(y) without a subscript for the common logarithm, i.e. base 10 assumed. [4] Hence, when a modern physical chemist reads, for example, Leo Szilard’s 1929 finding that the entropy produced by the measurement made by a Maxwell’s demon of the position of a gas particle in a two chamber system has the value:

The physical chemist may very well assume that Szilard is using a common logarithm, whereas in fact he is using a natural logarithm. [5] Subsequently, if the very same physical chemist next reads Gilbert Lewis' 1930 derivation on the same subject, finding that he calculates the entropy change to be: [6]

confusion may result on the puzzlement as to why Szilard is using common logarithms and Lewis is using natural logarithms, whereas in fact they are both using natural logarithms.

History

Logarithms were introduced by Scottish mathematician

Log.

as an abbreviation for "logarithm" first appears in the 1616

The so-called "ln" notation, the abbreviation ln short for natural logarithm, was, supposedly, first used in 1893 by American mathematician Irving Stringham (1847-1909) in his

References

1. Daintith, John. (2005).

2. Cajori, Florian. (2008). “Earliest Uses of Function Symbols.”, Jeff560.tripod.com.

3. Brown, Julian. (2002).

4. Mortimer, Robert G. (2005).

5. Szilárd, Leó. (1929). “On the Decrease in Entropy in a Thermodynamic System by the Intervention of Intelligent Beings” (Uber die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen),

6. Lewis, Gilbert. (1930). “The Symmetry of Time in Physics”,

External links

● Logarithm – Wikipedia.