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Common logarithm

from class:

Algebra and Trigonometry

Definition

A common logarithm is a logarithm with base 10. It is often written as $\log_{10} x$ or simply $\log x$.

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5 Must Know Facts For Your Next Test

  1. The common logarithm of a positive number $x$ is the exponent to which 10 must be raised to produce $x$.
  2. $\log_{10}(1) = 0$ because $10^0 = 1$.
  3. $\log_{10}(10) = 1$ because $10^1 = 10$.
  4. Common logarithms are used in many scientific and engineering fields due to their simplicity with base-10 calculations.
  5. Common logarithms can be calculated using scientific calculators, usually represented by the 'LOG' button.

Review Questions

  • What is the common logarithm of 100?
  • If $\log_{10}(x) = -2$, what is the value of $x$?
  • How do you represent the common logarithm of a number using a calculator?
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