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Mathematical Requirements (Appendix C)

Logarithmic scales and orders of magnitude

  • 5 things to know
  • All units

Overview

Recall questions on Logarithmic scales and orders of magnitude.

What you need to know

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Key term

When using a calculator for exponential functions, what key operations might you need?

Key term

What is the purpose of using logarithms for quantities that span several orders of magnitude?

Key term

On the Richter scale, what does an increase of one whole number represent in terms of measured amplitude?

Key term

How does a logarithmic scale differ from a linear scale in representing changes?

Numbers

State the formula that defines pH in terms of hydrogen ion concentration.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    How do equal intervals on a logarithmic scale differ from equal intervals on a linear scale?

    Model answer

    On a logarithmic scale, equal intervals represent equal ratios or multiplicative factors, whereas on a linear scale they represent equal differences.

  2. 2

    What is the purpose of using logarithms for quantities that span several orders of magnitude?

    Model answer

    Logarithms compress quantities spanning several orders of magnitude into a more manageable scale.

  3. 3

    How does a logarithmic scale differ from a linear scale in representing changes?

    Model answer

    A logarithmic scale represents equal multiplicative changes as equal intervals, so each step represents multiplication by a constant factor rather than addition of a constant amount.

  4. 4

    Give two real-world examples of logarithmic scales used in physics.

    Model answer

    The decibel scale for sound intensity and the Richter scale for earthquake magnitude.

  5. 5

    What does the logarithm to base 10 of a number tell you?

    Model answer

    It gives the power to which 10 must be raised to equal that number.

  6. 6

    When using a calculator for exponential functions, what key operations might you need?

    Model answer

    Power functions (xⁿ), exponential functions (eˣ or 10ˣ), and logarithmic functions (log and ln).

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