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Logarithms
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  1. Logarithms Math 3 Standard MM3A3

  2. Background: • Before there were calculators that could evaluate powers, mathematicians had to use logarithms • Logarithms are helpful especially when there are non-integer powers • For example:

  3. Definition: • The logarithm of x with base a • is denoted as: • This is read “log base a of x” • and defined as:

  4. Logarithmic form: Exponential form: Translate from logarithmic form to exponential form:

  5. Logarithmic form: Exponential form: Translate from exponential form to logarithmic form:

  6. Special Logarithms because because because

  7. Evaluate each logarithm

  8. Properties of Logarithms Math 3 MM3A2

  9. The Product Property • Example:

  10. The Quotient Property • Example:

  11. The Power Property • Example:

  12. Expansion • The properties are used to expand the logarithm • Each factor will have it’s own log • Example: Expand each logarithm

  13. Expansion • Example: Expand each logarithm

  14. You Try! • Expand the following logarithms using the properties of logarithms:

  15. Condense • The properties are used to condense the logarithm • There will be one single log • Example: Condense each logarithm

  16. Condense • Example: Condense each logarithm

  17. You Try! • Condense the following logarithms in to a single logarithm using the properties of logarithms: