Pre-Calculus 12 Notes

By: Gen L.

In partnership with Hyperion University, 2024

Lesson 2: Intro to Logarithms

The Logarithm

Remember the definition in Lesson 1?

  • We have many forms:
  • The Common Logarithm: (assume 10 if no base).
  • The Natural Logarithm: . This makes more sense in calculus.

Conversion

  • to Logarithmic Form
  • to Exponential Form

Evaluating

Logarithms answer the question: What power of results in ?

    • 2
    • 0
    • 4
    • -3
    • -5
    • 4
    • -2

Exponential Growth / Applications

  • Exponential Growth is a relatively rapid rate of growth. I mean, look at the graph of .
  • As a result, in some situations, a logarithmic scale is applied to deal with large numbers.

Applications I: Earthquakes

  • You may be familar with the Richter Scale, which measures the intensity of the earthquake.

Examples

  • Turkey in 1999 measured 7.4 on the Richter Scale, while Seatle in 1996 measured 5.3. How many times as intense was the Turkey earthquake?
  • Start with the difference, then exponentiate.
  • more intense

Working Backwards

  • If Earthquake A was measured at 2.5, and Earthquake B is 800 more intense, what is the measurement.
  • Start with the logarithm, then add.

Applications II: pH

Another example is the pH scale.

Example

  • A banana has a pH of 5.2, while vinegar has a pH of 2.3. How many times as acidic is the vinegar?
  • Same as Richter Scale.
  • more acidic.

Next Lesson