CA_GPS_29 - Express powers as factors. a) ), 4 2 ( log 3...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Rev. S08 http://faculty.valenciacc.edu/ashaw/ COLLEGE ALGEBRA NAME: ________________________________ GPS # 29 3.3 PROPERTIES OF LOGARITHMS 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” ) 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 = . 1. Write each expression as a sum and/or difference of logarithms.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Express powers as factors. a) ), 4 2 ( log 3 > + = x x x y b) 1 , 1 ln > ! ! " # $ $ % & = x x e y c) 5 , ) 5 ( 1 log 2 3 > ! " # $ % & + = x x x y d) 2 , ) 2 ( 1 3 ln 3 2 > ! ! " # $ $ % & + = x x x x y 2. Write each expression as a single logarithm. a) ) log( 4 ) log( C x y + = b) ) ln( ) ln( x e A y + = c) ) 1 ( log 7 ) ( log 4 ) 1 ( log 2 2 2 2 + ! + ! = x x x y d) ! " # $ % & + + ! " # $ % & = x x x x y 1 ln 1 ln 3. Use the Change-of-Base Formula to evaluate each logarithm. a) 25 log 3 b) e 5 log c) 51 log 2 d) 8 log !...
View Full Document

Ask a homework question - tutors are online