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Chapter 3

Chapter 3 . 3-3 Properties of logarithms. SAT Problem of the day. solution. Right Answer : A. objectives. Rewrite logarithms with different bases Use properties of logarithms to evaluate or rewrite logarithmic expressions

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Chapter 3

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  1. Chapter 3 3-3 Properties of logarithms

  2. SAT Problem of the day

  3. solution • Right Answer : A

  4. objectives • Rewrite logarithms with different bases • Use properties of logarithms to evaluate or rewrite logarithmic expressions • Use properties of logarithms to expand or condense logarithmic expressions

  5. Change of base formula While most scientific calculators have buttons for only the common logarithm and the natural logarithm, other logarithms may be evaluated with the following change-of-base formula. Change-of-base Formula

  6. Example#1 • Evaluate log5 3

  7. Properties of logarithms • The properties on the right are restatements of the general properties for the natural logarithm. • Many logarithmic expressions may be rewritten, either expanded or condensed, using the three properties above. Expanding is breaking down a complicated expression into simpler components. Condensing is the reverse of this process.

  8. Properties of logarithms • In less formal terms, the log rules might be expressed as: • 1) Multiplication inside the log can be turned into addition outside the log, and vice versa. • 2) Division inside the log can be turned into subtraction outside the log, and vice versa. • 3) An exponent on everything inside a log can be moved out front as a multiplier, and vice versa.

  9. Example#2 • Expand log3(2x).

  10. Example#3 • Expand log4( 16/x ).

  11. Example#4 Expand the following:

  12. Student guided practice • Do problems 1-6 in the worksheet

  13. Condensing logarithms • Simplify log2(x) + log2(y).

  14. Example#5 • Simplify log3(4) – log3(5).

  15. Example#6 • Simplify3log2(x) – 4log2(x + 3) + log2(y).

  16. Student guided practice • Do odd problems 13-20 in your worksheet

  17. Homework!! • Do problems 47-51 and 69-73 in your book page 207 and 208

  18. Closure • Today we learned about properties of logarithms • Next we are going to learn how to solve exponential and logarithm functions

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