In mathematics, a base is the number that is raised to a power in an exponential expression. It serves as the foundation for representing numbers in different numeral systems.
congrats on reading the definition of base. now let's actually learn it.
The base in an exponentiation expression such as $a^b$ is $a$.
Bases are fundamental in logarithmic functions where $\log_b(x)$ involves base $b$.
In various numeral systems, such as binary (base 2) and decimal (base 10), the base determines the number of digits and their values.
The change of base formula for logarithms is $\log_b(a) = \frac{\log_k(a)}{\log_k(b)}$, where $k$ is any positive number.
The base affects the shape and growth rate of exponential functions.
Review Questions
What is the base in the expression $5^3$?
How do you apply the change of base formula for logarithms?
In which numeral system does base 2 operate?
Related terms
Exponent: The exponent indicates how many times the base is multiplied by itself.
Logarithm: The logarithm is the inverse operation to exponentiation, representing the power to which a given base must be raised to obtain a certain number.
Numeral System: A mathematical notation for representing numbers using a set of digits or symbols, with its structure determined by its base.