Definition:General Logarithm/Common/Notation for Negative Logarithm

Definition

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

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

$a \times 10^{-d}$

where $d \in \Z_{>0}$ is a (strictly) positive integer.

Let $\log_{10} n$ denote the common logarithm of $n$.

Then it is the standard convention to express $\log_{10} n$ in the form:

$\log_{10} n = \overline d \cdotp m$

where $m := \log_{10} a$ is the mantissa 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: Example 3.