7.3-7.5 Logarathmic Functions

7.3-7.5 Logarathmic Functions - Common and Natural...

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Unformatted text preview: Common and Natural Logarithmic Functions Sections 7.3-7.5 • Common logarithms: log v = u iff • 10 = v u Natural logarithms: ln v = u iff e =v u 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. log10 k = k and ln e k for k = every real number k. • 4. 10 log v = v and e ln v for every v > 0. =v Laws of Logarithms • For all v, w > 0 log b (vw) = log b v + log b w ln(vw) = ln v + ln w log(vw) = log v + log w v g b ÷ = log b v − log b w w v ln ÷ = ln v − ln w w log b v = k log b v k ln v = k ln v k Change of Base Formula • For any positive number v, log v log b v = log b log b v = log v log ln v log b v = ln b Solving Equations • For all real numbers b > 0, If u = v, then b = b n v If u = v, then log b u = log b v • The converse is also true. 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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7.3-7.5 Logarathmic Functions - Common and Natural...

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