CA_GPS_28 - f . * Natural logarithmic function: y = log e (...

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Rev. S08 http://faculty.valenciacc.edu/ashaw/ PRECALCULUS NAME: ________________________________ GPS # 28 3.2 LOGARITHMIC FUNCTIONS II Class Time: ____________ Date: __________ Useful Guidelines: * The logarithmic function to the base a , where 0 > a and 1 ! a : y = log a ( x ) if and only if y a x = ; * Properties of the logarithmic Function y = log a ( x ) (where 0 > a and 1 ! a ): (1) Domain: the interval ) , 0 ( ! ; Range: the interval ) , ( ! "! ; (2) x -intercepts: 1; y -intercept: none; (3) Vertical asymptote: 0 = x ; (4) f ( x ) = log a ( x ), a > 1 , is an increasing, one-to-one, smooth and continuous function; f ( x ) = log a ( x ),0 < a < 1 , is a decreasing, one-to-one, smooth and continuous function; (5) The points ), 1 , ( ), 0 , 1 ( a and ) 1 , ( 1 ! a are always on the graph of
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Unformatted text preview: f . * Natural logarithmic function: y = log e ( x ) = ln( x ) if and only if y e x = . * Common logarithmic function: y = log( x ) if and only if y x 10 = . 1. Graph each logarithmic function. a) y = log( x ) b) y = ln( x ) c) y = log 3 ( x ) d) y = log 5 ( x ) 2. Use transformations to graph each function. Determine the domain, range, and vertical asymptote of each function. a) ) 2 log( ) ( ! = x x f b) ) 9 ln( + = x y 3. Solve each equation. a) log 3 ( x ) = 4 b) 2 ) 1 ( log 5 = + x c) ln( x ) = 3 d) ln( e x ) = 4 e) 5 2 = x e f) 10 3 = ! x e...
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