# OSU MTH 111 - Act-#17 Log Ftns-Key (6 pages)

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## Act-#17 Log Ftns-Key

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- Pages:
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- School:
- Oregon State University
- Course:
- Mth 111 - College Algebra

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Name Key Grp Math 111 Logarithmic Functions GrpAct 17 Prerequisite Skills Key Terms working with inverse functions composing functions with their inverse working with exponential functions Logarithmic Function Natural Logarithm Common Logarithm Logarithm Properties Inverse Properties for Logs Change of Base Property Exact Approximate solutions Sects 5 4 5 5 Learning Outcomes Convert between exponential and logarithmic statements Evaluate logarithmic expressions Apply change of base formula to logarithmic expressions Use logarithms to solve exponential equations Use exponentiation to solve logarithmic equations Determine domain range of logarithmic functions Apply the properties of logarithms to simplify or expand logarithmic expressions Model with logarithmic functions x 1 1 Last class we talked about exponential functions Let f x 4 x and g x Evaluate each of the following 5 1 25 d g 2 25 a g 2 b f 0 5 2 c f 3 e f 0 1 f g 0 1 1 64 p is the Power that goes on the Base b to give you m 2 This class we ll look at logarithmic functions In your MML HW and Reading you saw how exponential and logarithmic equations are related Fill in the table with the alternate forms of each equation Exponential Form Logarithmic Form Written Form 1 log 5 2 25 The base 5 to the 2 power is equal to 23 8 log 2 8 3 The base 2 to the 3 power is equal to 8 43 64 log 4 64 3 811 4 3 log 81 3 5 2 7 1 1 25 1 7 1001 2 10 The base 4 to the 3 power is equal to 64 1 4 1 log 7 1 7 log100 10 1 2 130 1 log13 1 0 by x log b x y e3 4657 32 1 25 ln 32 3 4657 see note below The base 81 to the 1 power is equal to 3 4 The base 7 to the 1 power is equal to The base 100 to the 1 7 1 power is equal to 10 2 The base 13 to the 0 power is equal to 1 The base b to the y power is equal to x The base e to the 3 4657 power is equal to 32 Don t know what ln means It is the logarithm with base e ln x loge x This logarithm is used a lot in mathematics and it is called the natural logarithm Do you remember last week when we

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