02Exponential and Logarithmic Functions

02Exponential and Logarithmic Functions - EXPONENTIAL AND...

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E XPONENTIAL AND L OGARITHMIC F UNCTIONS Rational Exponents ( 29 q p q p p q q p q p n n n b b b b b b b b b b 1 1 .... = = = = × × = - - ( 29 pq q p q p q p q p q p b b b b b b b b b = = = = - + 1 0 Note: 0 b to avoid imaginary values Exponential Functions Exponential function with base b: x b x f = ) ( where 1 , 0 b b (constant base and variable exponent). Note! 6 ) ( x x f = is not an exponential function, since the base is a variable and the exponent is constant. for Exponential functions are continuous. There are only two shapes (b>1 and b<1). The domain is ( 29 - , and the range is ( 29 , 0 . 1 0 < < = b b y x 1 = b b y x 1 ) ( 1 1 = = = x f b b x
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Logarithms x b log Logarithm to the base b of x is the exponent to which b must be raised to produce x x b x b = log for x > 0 Logarithms can be common ( a a log log 10 = ) or natural ( a a e ln log = ) where e = 2.7182…. . e
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02Exponential and Logarithmic Functions - EXPONENTIAL AND...

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