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4.2 LogarithmicFunctions

# 4.2 LogarithmicFunctions - MAC2233(3.4 North FIU MDC 4....

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MAC2233 (3.4) FIU, MDC- North 4.2 Logarithmic Functions The inverse function of  y = f(x) = a x   is   x = a y , which is equivalent to   the logarithmic function  y = log  a  x .   This  equivalence is used to convert between logarithmic and exponential functions.  If the base is the number  e , then  x = e  if and only if  y = ln x .   Properties of common and natural logarithms:   (1)  log b  1 = 0  ,  log b b = 1   (b   1, b > 0) ,   ln1 =  0,  and  ln e = 1  (2)  = b log M b M = r b log b r b e b ln = and  ln e b  = b and if    u  and  v   are any positive numbers, then (3)  Equality Rule:    = = b b log u log v u v   (4)  Product Rule:   ( 29 = + b b b log uv log u log v ; (5)  Power Rule:   = r b b log u r log u ; (6)  Quotient Rule:   = - b b b u log log u log v v ;  (7)  Conversion formulas:  b a b log M log M log a =   and   a ln M log M ln a = .

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4.2 LogarithmicFunctions - MAC2233(3.4 North FIU MDC 4....

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