Pre-Calculus 12 Notes

By: Gen L.

In partnership with Hyperion University, 2024

Lesson 4: Laws of Logs II

Previously

  1. The Product Law:
  2. The Quotient Law:
  3. The Power Law:
  4. The Identity Law:
  • But, what if you need a single log, and they aren't all logs?

Combining Complex Logs

Rewrite as one log:

The Idea of Basis

  • Logs have a 'basis', which is the base of the exponential.
  • On most calculators, there is no way to find logs for other bases.
    • So, how do we solve it then?
  1. Change of Basis Law:

Using Change of Basis

Easier Simplification

To simplify easier, we have another law:

  1. Inverse Laws:
  • For example:

Substitution Questions

If and , express the following in terms of x and y:

Substitutions, cont.

If and , express the following in terms of a and b:

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