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Base

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Algebra and Trigonometry

Definition

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.

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5 Must Know Facts For Your Next Test

  1. The base in an exponentiation expression such as $a^b$ is $a$.
  2. Bases are fundamental in logarithmic functions where $\log_b(x)$ involves base $b$.
  3. In various numeral systems, such as binary (base 2) and decimal (base 10), the base determines the number of digits and their values.
  4. The change of base formula for logarithms is $\log_b(a) = \frac{\log_k(a)}{\log_k(b)}$, where $k$ is any positive number.
  5. 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?
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