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Article 11 — Appendix A.23

ln — natural logarithmic function

Category. Mathematics.

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

References. This article is a part of scientific calculator Li-L, scientific calculator Li-X, scientific calculator Li-Lc and scientific calculator Li-Xc products.

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 singular point. Function graph is depicted below — fig. 1.

Fig. 1. Graph of the natural logarithmic function y = ln x 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]);