The Art of Interface

# log or lg — decimal logarithmic function

Category. Mathematics.

Abstract. Decimal logarithm: definition, graph, properties and identities.

## 1. Definition

Decimal logarithmic function is the inverse of the 10-base exponential function

10x

## 2. Graph

Decimal logarithmic function is defined on positive part of the real axis — so, its domain is (0, +∞). 0 is singular point. Function graph is depicted below — fig. 1. Fig. 1. Graph of the decimal logarithmic function y = logx.

Function codomain is entire real axis.

## 3. Identities

By definition:

log10xx

Reciprocal argument:

log(1/x) = −logx

Product and ratio of arguments:

log(xy) = logx + logy
log(x /y) = logx − logy

Power of argument:

logxa = a logx

Base change:

logax = logx /loga
logax = logbx /logba

## 4. Support

Decimal logarithmic function log or lg is supported in:

Decimal logarithmic function of the complex argument log or lg is supported in:

## 5. How to use

To calculate decimal logarithm of the number:

``log(2);``

To calculate decimal logarithm of the current result:

``log(Rslt);``

To calculate decimal logarithm of the number x in memory:

``log(Mem[x]);``