# What is a common logarithm or common log?

##### 2 Answers

The inverse of the function

#### Explanation:

The function:

#f(x) = 10^x#

is a continuous, monotonically increasing function from

graph{10^x [-2.664, 2.338, -2, 12.16]}

Its inverse is the common logarithm:

#f^(-1)(y) = log_10(y)#

which as a result is a continuous, monotonically increasing function from

graph{log x [-1, 12.203, -1.3, 1.3]}

Note that the exponential function satisfies:

#10^a * 10^b = 10^(a+b)#

Hence its inverse, the common logarithm satisfies:

#log_10 xy = log_10 x + log_10 y#

As detailed below.

#### Explanation:

common logarithm is the logarithm with base 10.

It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as "standard logarithm".

Historically, it was known as logarithmus decimalis or logarithmus decadis. It is indicated by

On calculators, it is usually "log", but mathematicians usually mean natural logarithm (logarithm with base e ≈ 2.71828) rather than common logarithm when they write "log".

To mitigate this ambiguity, the ISO 80000 specification recommends that **lg (x)** and **ln (x)**.