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Understanding Logarithms: Properties, Applications, and Practice Problems

This lesson focuses on Section 7.5: Properties of Logarithms. We will review previous assignments and explore key vocabulary terms like exponentials and logarithms. You will learn important properties including the product, quotient, and power properties of logarithms, along with the one-to-one property of exponential functions. Practice problems will be provided to help you combine and simplify logarithmic expressions. Don't forget to review resources available at mrwaddell.net and complete the assigned exercises at the end: Chapter 7.5: 15-30 and 33-42, picking 10 problems from each section.

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Understanding Logarithms: Properties, Applications, and Practice Problems

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  1. WarmupAlg222 Mar 2012

  2. Agenda • Don't forget about resources on mrwaddell.net • Assignment from last class period • Sect 7.5: Properties of logarithms

  3. Go over assignment from last class period

  4. Section 7.5: Properties of Logarithms

  5. Vocabulary • Exponentials • Logarithm • log x • ln x Any equationof the form x=(b)y The opposite of an exponential equation • y= logbx No base? It is automatically base 10! “ln” is a shortcut way to write loge said “log base e”

  6. Property of Logs and Exponents • One-to-One Property of Exponential Functions and logs • If bx= by, thenx = y. If logbx = logby, thenx = y.

  7. Exponents First – Page 330

  8. Exponents First

  9. Product Property logb(nm) = = logbn+ logbm

  10. logb= n m Quotient Property = logbn– logbm

  11. Power Property logbmp = = plogbm THIS IS EASILY THE MOST IMPORTANT ONE!

  12. Inverse Properties (2 of them) logbbx = x

  13. Practice Problems Write each expression as a single logarithm. Then simplify if possible. problem log25 + log27 product property log2 (5∙7) finished log2 (35)

  14. Practice Problems Write each expression as a single logarithm. Then simplify if possible. problem Log536x3 product property Log536 + Log5x2 Power property Log536 + 2Log5x

  15. Practice Problems Write each expression as a single logarithm. Then simplify if possible. problem quotient property product property power property

  16. Practice Problems Write each expression as a single logarithm. Then simplify if possible. problem log48 + log42 product property log4(16) Hmm, what exponent for 4x =16 log4 (4∙4) 2 is the answer!

  17. Practice Problems Write each expression as a single logarithm. Then simplify if possible. problem log335 - log5125 power prop & factoring 5log33 – log5(5∙5∙5) Inverse prop 5 – log5(5∙5∙5) How many 5’s are there again? 5 – 3 2 is the answer!

  18. Assignment • Chapter 7.5: 15-30, • 33 – 42, • Pick 10 from each section

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