5.4,5.5,5.6 Logarithmic Functions

# 5.4,5.5,5.6 Logarithmic Functions - v log log log b v v =...

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Common and Natural Logarithmic Functions Sections 5.4, 5.5 and 5.6

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Common logarithms: Natural logarithms: log 10 u v u iff v = = ln u v u iff e v = =
Basic Properties of Logarithms 1. log v and ln v are defined only when v > 0. 2. log 1 = 0 and log 10 = 1 ln 1 = 0 and ln e = 1 3. for every real number k . 4. for every v > 0. log10 ln k k k and e k = = log ln 10 v v v and e v = =

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Laws of Logarithms For all v , w > 0 log( ) log log vw v w = + log ( ) log log b b b vw v w = + ln( ) ln ln vw v w = + og log log b b b v v w w = - ÷ ln ln ln v v w w = - ÷ log log k b b v k v = ln ln k v k v =
Change of Base Formula For any positive number

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Unformatted text preview: v , log log log b v v = log log log b v v b = ln log ln b v v b = Solving Equations • For all real numbers b > 0, • The converse is also true. , n v If u v then b b = = , log log b b If u v then u v = = Joke Time • What do you call a funny lizard? • A silly-mandar Submitted by Natalie Williams • What do you call a smart lizard? • A geek-o Submitted by Caroline Morris...
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5.4,5.5,5.6 Logarithmic Functions - v log log log b v v =...

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