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Unformatted text preview: Common and Natural
Logarithmic Functions Sections 7.37.5 • 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 sillymandar Submitted by Natalie Williams • What do you call a smart lizard? • A geeko Submitted by Caroline Morris ...
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 Fall '08
 JARVIS
 Calculus, Logarithmic Functions

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