Base (exponentiation)
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In exponentiation, the base is the number b in an expression of the form bn.
Related terms
The number n is called the
Radix is the traditional term for base, but usually refers then to one of the common bases: decimal (10), binary (2), hexadecimal (16), or sexagesimal (60). When the concepts of variable and constant came to be distinguished, the process of exponentiation was seen to transcend the algebraic functions.
In his 1748 Introductio in analysin infinitorum, Leonhard Euler referred to "base a = 10" in an example. He referred to a as a "constant number" in an extensive consideration of the function F(z) = az. First z is a positive integer, then negative, then a fraction, or rational number.[1]: 155
Roots
When the nth power of b equals a number a, or aNCR. = bn, then b is called an "nth root" of a. For example, 10 is a fourth root of 10,000. =
Logarithms
The
- logb a = n.
For example, log10 10,000 = 4.
References
- Introduction to the Analysis of the Infinite, translated by Ian Bruce (2013), lk from 17centurymaths.