CA_GPS_30

# CA_GPS_30 - ln ln log a M M a = If N M = then log log N M a...

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Rev. S08 http://faculty.valenciacc.edu/ashaw/ COLLEGE ALGEBRA NAME: ________________________________ GPS # 30 3.3 PROPERTIES OF LOGARITHMS II Class Time: ____________ Date: __________ Useful Guidelines: Properties of Logarithms : 0 > M and 0 > N The logarithmic function to the base a , where 0 > a and 1 ! a : x y a log = if and only if y a x = ; The logarithmic function to the base b , where 0 > b and 1 ! b : x y b log = if and only if y b x = ; * 0 ) 1 ( log = a ; 1 ) ( log = a a ; log a ( M r ) = r log a ( M ) 0 ) 1 ln( = ; 1 ) ln( = e ; ln( e 2 ) = 2ln( e ) = 2 ; ln( e x ) = x * M a M a = ) ( log x e x = ) ln( * ) ( log ) ( log ) ( log N M MN a a a + = ) ln( ) ln( ) ln( N M MN + = * ) ( log ) ( log log N M N M a a a ! = " # \$ % ) ln( ) ln( ln N M N M ! = " # \$ % * ) ( log ) ( log ) ( log a M M b b a = “Change-of-Base Formula”
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Unformatted text preview: ) ln( ) ln( ) ( log a M M a = * If N M = , then ) ( log ) ( log N M a a = ; If ) ( log ) ( log N M a a = , then N M = . Solve each equation and give the solution set. 1. a) 2 ) 5 ( log ) 2 ( log 5 5 = + x b) ln( x " 1) " 2ln(4) = ln( e 2 ) + ln(1) 2. a) 1 ) 2 ( log ) ( log 3 3 = ! + x x b) ln( x + 3) " ln( x ) = ln( e 4 ) 3. a) 10 3 = x b) x x 5 2 2 = + 4. Evaluate the following: a) = ) ( log 3 3 k b) = ) ( log 7 7 ! c) = ) ln( k e d) = ) ln( e...
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