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Math 148 Exponentials and Logarithms Review Activities with Exponents 1. () 1 1 11 1 1 22 2 2 −− ⎛⎞ == = ⎜⎟ ⎝⎠ 2. 1 n nn m n m mm a aa a a =⋅ = 3. a. F – Violation of Order of Operations b. T c. T d. F Graphs 1. () l o g f xx = Domain: (0, ) Range: ( ) , −∞∞ () 1 0 x fx = Domain: , −∞ ∞ Range: (0, ) 2. ,, 0 ABC > Activities with Logarithms 1. a. F b. F c. T d. F e. F f. T g. F h. T i. T j. T k. F l. F m. F 2. a > 0: Use the definition of logarithms for the second part. 3. a. Rule 1 b. Rule 2 c. Rule 5 4. log log log log B mA B m A =⇒ = : log ( ) A mB = so log log ( ) log A B B A = You can find any logarithm that you need to just by using ln or log . Additional Exercises 1. ln 40 2 1 160 t ft e = , 40 a = 3. 4log( 4) log 4 log( 4) log( 4) 71 log( 4) log 4 log( 4) x + + 2. 1l n 5 ln 2 3 x =

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Additional Activities 1. A student solves a logarithmic equation as follows: Given: ) 24 log( ) 2 log( ) log( = + x x Solution: Use the properties of logarithms to get 24 log )] 2 ( log[ = x x Now divide by log and cancel to get the following result: ( )( ) 0 4 6 0 24 2 24 2 24 ) 2 ( 2 2 = + = = = x x x x x x x x So we have that
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