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Evaluate Logarithms

Evaluate Logarithms

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Evaluate Logarithms

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  1. Evaluate Logarithms Notes 12 – Section 7.4

  2. Essential Learnings • Students will understand and be able to evaluate exponential functions using logarithms. • Students will be able to recognize and use equivalent representations of expressions.

  3. Logarithm with Base b Let band ybe positive numbers with b≠1. The logarithm of ywith base b is defined as follows: if and only if “Log base b of y”

  4. Common Logarithm Logarithm with base 10: Logarithm with base e: “natural log”

  5. Example 1 (3-6) Rewrite the logarithm into exponential form.

  6. Example 2 (3-6) Rewrite the logarithm into exponential form.

  7. Example 3 (3-6) Rewrite the logarithm into exponential form.

  8. Class Problems Rewrite each logarithm into exponential form.

  9. Example 4 (8-19) Evaluate the logarithm without a calculator (change from logarithmic form to exponential form).

  10. Example 5 (8-19) Evaluate the logarithm without a calculator (change from logarithmic form to exponential form).

  11. Example 6 (8-19) Evaluate the logarithm without a calculator (change from logarithmic form to exponential form).

  12. Class Problems Evaluate the logarithm without a calculator (change from logarithmic form to exponential form).

  13. Calculating Logarithms (20-27) Use a calculator to evaluate the logarithm.

  14. Exponential vs. Logarithmic • How are logarithmic functions related to exponential functions? They are inverse functions.

  15. Inverse Properties of Logarithms

  16. Example 7 (29-35) Simplify the expressions using inverse properties.

  17. Example 8 (29-35) Simplify the expressions using inverse properties. The log is base 2, so change 16 into 24 to simplify.

  18. Example 9 (29-35) Simplify the expressions using inverse properties. The log is base 3, so change 81 into 34 to simplify.

  19. Assignment Pages 503: 3–6, 8–19, 20, 23, 24, 26, 27, 29–35 odd MM 3-1 – Due Tuesday/Wednesday Tuesday ICE – Finish Mastery Assignment Unit Study Guide 5 – Keep working on it!