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Logarithmic and Exponential Properties: A Comprehensive Review with Example Questions

Dive into the rich world of logarithms and exponentials with this lesson that reviews key properties. Explore the fundamental rules, including how to add and subtract exponents when multiplying and dividing numbers with the same base. Engage with practical examples, including finding capitals like Damascus and Kinshasa, to reinforce your understanding of logarithmic functions. Review various equation-solving techniques using natural and common logarithms. Complete practice exercises to solidify your knowledge and prepare for applied mathematical challenges.

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Logarithmic and Exponential Properties: A Comprehensive Review with Example Questions

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Presentation Transcript

  1. Mini-Theme – Capitals! Lesson 37: Log and Ln properties

  2. Review Answers

  3. What is the capital of Syria? • Damascus

  4. Follow up on Warm Up • Solve using ln and exponential rules • Solve using the intersection on the calc

  5. Proofs of ln and log properties • Pick any two numbers M and N. • Show that: • This goes back to the old exponential properties. • When multiplying same base – add exponents • When dividing same base – subtract exponents

  6. How do we expand log and ln? • Example: Expand • More examples…..

  7. Kinshasa is the capital of what African country? • The Democratic Republic of the Congo

  8. Prove Exponent Multiplicative Property • Show with numbers – choose a number for M and k. • This is also a repeat of the exponent property • When you raise a power to a power you multiply • Examples….

  9. Practice:

  10. CFU • What is the capital of Wisconsin? • Who wrote the constitution? • Who was the 4th President of the US?

  11. Equation Solving • Two ways to solve equations • Take the ln or log of both sides then solve • Rewrite as an ln or log then solve • First we need to review the change of base property • Solve each of these:

  12. Solving both ways

  13. Homework • These are pictures from what capital city of Malaysia?

  14. Homework

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