Math Notes

10/17/08

4.3 Logarithmic Functions * y= log a x if and only if x=ay Logarithms & exponential Functions are inverses

Change each exponential expression to a Log equation 1. 53=125 2. e√2 = π Log 5125=3 Ln π= √2 u v * If a =a , then u=v Find the exact value of log 28=x 2x=8 2x=23 X=3 Find the exact value of log √24=x √2x =4 (21/2) x = 4 (21/2) x = 22 2(1/2x=2)2 x=4 *Domain of a logarithmic function= Range of an exponential function= (0, ω) *Domain of an exponential function=Range of a logarithmic function= (-ω,ω) Graph y=log(x) D :( 0,ω) R :( - ω,ω) V.A. x=0 Find the domain of each Logarithmic function: Range, vertical asymptote

1. F(x) =log 2(1-x) =log 2(-x+1) D: (-ω, 1) R: (-ω,ω) V.A. x=1

2. y= Ln (1/2x) (1/2x>0)

D: X>0 R: (-ω,ω) V.A. X=0

1-x >0