Lesson 2 Solutions

Lesson 2 Solutions - Notation log a x = log a ( x ) ln x =...

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Unformatted text preview: Notation log a x = log a ( x ) ln x = log e ( x ) lg x = log 10 ( x ) lb x = log 2 ( x ) Note: If there is a problem written log x , assume that the base is not required to awnser the question (It will cancel out-Please check with me if it doesnt). Rules for Logarithms log a ( xy ) = log a ( x ) + log a ( y ) log a x y = log a ( x )- log a ( y ) log a ( x y ) = y log a ( x ) log a ( a x ) = a log a ( x ) = x log a (1) = 0 log a ( x ) = 1 log x ( a ) log a ( x ) log a ( y ) = log y ( x ) log a b ( x y ) = y b log a ( b ) WARNING: In log a b , both a AND b must be positive. Also log a (1) = 0 means that log 1 ( a ) is undefined and log 1 (1) is multi-valued. Problem Set 1. Solve for x : log (8) = x log (4) log (8) = x log (4) log (2 3 ) = x log (2 2 ) 3log (2) = 2 x log (2) 3 = 2 x x = 3 2 2. Solve for x ( x > 1): log 3 ( x- 1) + log 3 ( x + 1) = 2 log 3 ( x- 1) + log 3 ( x + 1) = 2 log 3 (( x- 1)( x + 1)) = 2 ( x- 1)( x + 1) = 3 2 3. What is the sum of the following series?3....
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This note was uploaded on 03/22/2010 for the course MATH 1104 taught by Professor Unknown during the Fall '10 term at Carleton.

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Lesson 2 Solutions - Notation log a x = log a ( x ) ln x =...

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