Definition:General Logarithm/Common/Characteristic

Definition

Let $n \in \R$ be a positive real number such that $0 < n < 1$.

Let $n$ be presented (possibly approximated) in scientific notation as:

$a \times 10^d$

where $d \in \Z$ is an integer.

Let $\log_{10} n$ be expressed in the form:

$\log_{10} n = \begin {cases} c \cdotp m & : d \ge 0 \\ \overline c \cdotp m & : d < 0 \end {cases}$

where:

$c = \size d$ is the absolute value of $d$

$m := \log_{10} a$

$c$ is the characteristic of $\log_{10} n$.

Sources

• 1972: Murray R. Spiegel and R.W. Boxer: Theory and Problems of Statistics (SI ed.) ... (previous) ... (next): Chapter $1$: Logarithms
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): characteristic: 1.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): logarithm (log)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): characteristic: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): logarithm (log)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): characteristic