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Mathematical Requirements (Appendix C)

Working with base-ten logarithms

  • 3 things to know
  • All units

Overview

Recall questions on Working with base-ten logarithms.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

State the relationship between a number x, its base-10 logarithm y, and powers of 10.

Process

Describe the process of converting a value to a logarithmic scale.

Numbers

Calculate the logarithm of value when value = 977222.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    How does a logarithmic scale differ from a linear scale in terms of what equal spacings represent?

    Model answer

    On a logarithmic scale, equal spacings represent equal multiplicative factors; on a linear scale, equal spacings represent equal additive amounts.

  2. 2

    What does the logarithm (base 10) of a quantity tell you?

    Model answer

    It gives the power of 10 needed to produce that quantity.

  3. 3

    State the relationship between a number x, its base-10 logarithm y, and powers of 10.

    Model answer

    If log₁₀(x) = y, then 10^y = x.

  4. 4

    Describe the process of converting a value to a logarithmic scale.

    Model answer

    Calculate the logarithm (base 10) of the quantity.

  5. 5

    Calculate the logarithm of value when value = 977222.

    Model answer

    Logarithm of value = log10(977222) = 5.99.

  6. 6

    Give an example of a real-world logarithmic scale used to measure sound intensity.

    Model answer

    The decibel scale.

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