The Art of Interface

# ln — natural logarithmic function

Category. Mathematics.

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

## 1. Definition

Natural logarithmic function is the inverse of the exponential function.

## 2. Graph

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

Function codomain is entire real axis.

## 3. Identities

By definition:

ln exx

Reciprocal argument:

ln(1/x) = −lnx

Product and ratio of arguments:

ln(xy) = lnx + lny
ln(x /y) = lnx − lny

Power of argument:

lnxa = a lnx

Base change:

logax = lnx /lna
logax = logbx /logba

## 4. Support

Natural logarithmic function ln is supported in:

Natural logarithmic function of the complex argument ln is supported in:

## 5. How to use

To calculate natural logarithm of the number:

``ln(2);``

To calculate natural logarithm of the current result:

``ln(Rslt);``

To calculate natural logarithm of the number x in memory:

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