The common logarithm is a logarithm having base ten. While logarthims to base 10 do not have any special mathematical properties, this logarithm is used in some formulas due to the decimal numbering system in use.
In physics and engineering, the notation usually denotes the common logarithm. However, mathematicians typically reserve that notation for the natural logarithm and would write the common logarithm explicitly as . Another notation sometimes used for the common logarithm is .
The common logarithm was created to accommodate our base ten, or decimal, numbering system.
Because the place value of each digit in a decimal number is ten times greater than that of the digit to its immediate right, the base-ten logarithm is a "common," or likely, use of logarithms in interpreting numerical expressions and their growth rates.
Logarithms of other bases become necessary as the specific exponential function necessitates. In higher-level mathematics such as calculus, the natural logarithm has more practical use due to its use of Euler's number, e.