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Evaluate Logarithms

Evaluate Logarithms. Notes 12 – Section 7.4. 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. Logarithm with Base b.

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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!

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