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Chapter 3.4 Properties of Log Functions

Chapter 3.4 Properties of Log Functions. Learning Target: I can find the inverses of exponential functions, common logarithms (base 10), natural logarithms (base e), graphs of logarithmic functions, and measuring sound using decibels. Properties of Logs.

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Chapter 3.4 Properties of Log Functions

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  1. Chapter 3.4Properties of Log Functions Learning Target: I can find the inverses of exponential functions, common logarithms (base 10), natural logarithms (base e), graphs of logarithmic functions, and measuring sound using decibels

  2. Properties of Logs • Product Rule: logb(RS) = logb R + logb S • Quotient Rule: logb (R/S) = logb R – logb S • Power Rule: logb (Rc)= c logbR

  3. Example • Expand the log of a product • Log (8xy4) • Expand the log of a quotient • ln[(x2 + 5)1/2/x]

  4. Changing the base • Graph y = log4 7. What problem do you have? Is there a log4 button on your calculator? • The following steps will give us a method for changing the base to something more desirable. • 4y = 7 • ln 4y = ln 7 • y ln 4 = ln 7 • y = ln 7/ ln 4

  5. Thus the Change of Base Formula • Logbx = lnx/lnb

  6. Homework Pg. 317 # 3 – 45 every 3rd

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