The Helpful Mathematics
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Article 11 — Appendix A.20

exp — exponential function

Category. Mathematics.

Abstract. Exponent: 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

Exponential function is the function of kind


where constant e is selected so that slope of the function at point x = 0 is 45°.

2. Graph

Exponential function is defined everywhere on real axis. Its graph is depicted below — fig. 1.

Fig. 1. Graph of the exponential function y = exp x Fig. 1. Graph of the exponential function y = ex.

Function codomain is positive half of the real axis: (0, +∞).

3. Identities

By definition:


Negative argument:

ex = 1 /ex

Sum and difference of arguments:

ex + y = ex ey
exy = ex/ey

Product of arguments:

exy = (ex)y

Base change:

ax = ex lna

4. Support

Exponential function exp is supported in:

Exponential function of the complex argument exp is supported in:

5. How to use

To calculate exponent of the number:


To calculate exponent of the current result:


To calculate exponent of the number x in memory: