The Helpful Mathematics
+38 044 572 93 47

Article 11 — Appendix A.22

log or lg — decimal logarithmic function

Category. Mathematics.

Abstract. Decimal 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

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 = log x Fig. 1. Graph of the decimal logarithmic function y = logx.

Function codomain is entire real axis.

3. Identities

By definition:

log10x ≡ x

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]);