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Math 148 Exponentials and Logarithms Review Activities with Exponents 1. ! " 1 1 1 1 1 1 2 2 2 # # # # \$# % ( ) * + 2 2. 1 n n n m m m a a a a a a a # # \$ \$ n m 3. a. F – Violation of Order of Operations b. T c. T d. F Graphs 1. ( ) log f x x Domain: (0 Range: , ) , ! " , #, , ( ) 10 x f x Domain: Range: (0 ! , #, ," , ) , 2. , , 0 A B C - Activities with Logarithms 1. a. F b. F c. T d. F e. F f. F g. T h. F i. T j. F k. F l. F 2. a > 0: Use the definition for second part. 3. a. Rule 1 b. Rule 2 c. Rule 5 4. log log log log B m A B m A . : log ( ) A m B 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. ln40 2 1 ( ) 160 t f t e % \$ ( ) * + , 40 a 3. 1 1 4log( 4) log4 log( 4) log( 4) 2 2 x x x # # # # # / 2. 1 ln5 ln2 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: 0 Use the properties of logarithms to get 24 log )] 2 ( log[ # x x 0 Now divide by log and cancel to get the following result: ! "! " 0 4 6 0 24 2 24 2 24 ) 2 ( 2 2 / # 1 # # 1 # 1 # x x x x x x x x 0 So we have that
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Unformatted text preview: and 6 ’ # x 4 ’ / x So the solutions are 6 and -4. Mistakes: 1. We don’t divide by log. 2. Must eliminate -4. 2. A student has to solve a system of equations ) 1 log( 2 3 # ’ # # ’ x y x y . He decides to graph both equations. The student then copies the following diagram to his worksheet. a. What is wrong with his diagram? Graph of log( 1) x # is graphed incorrectly 1. It goes through the point (2,0) 2. The left-side of the graph doesn’t end b. Will the two graphs have an intersection? Yes c. Will the solution (if there is one) be less than or greater than 1? Explain how you know that, without actually drawing more of the diagram. Must be greater than 1 since the domain of log( 1) x # is ! " 1, ,...
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