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Common logarithm

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College Algebra

Definition

A common logarithm is a logarithm with base 10, often written as $\log_{10}(x)$ or simply $\log(x)$. It is commonly used in scientific calculations and when dealing with exponential growth or decay.

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5 Must Know Facts For Your Next Test

  1. The common logarithm of 10 is 1, i.e., $\log(10) = 1$.
  2. The common logarithm of 1 is 0, i.e., $\log(1) = 0$.
  3. Common logarithms are the inverse functions of base-10 exponential functions.
  4. The change of base formula allows conversion between natural logarithms and common logarithms: $\log_a(b) = \frac{\log(b)}{\log(a)}$.
  5. $\log(xy) = \log(x) + \log(y)$ and $\log(\frac{x}{y}) = \log(x) - \log(y)$ are key properties used to simplify expressions.

Review Questions

  • What is the value of $\log_{10}(100)$?
  • How can you express $\ln(x)$ in terms of common logarithms using the change of base formula?
  • Simplify the expression: $\log(2) + \log(5)$.
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