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mac1147_lecture14_1_b - L14 Exponential and Logarithmic...

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183 L14 Exponential and Logarithmic Functions Statement : If a and x are real numbers with 0 a > and 1 a , then x y a = is a uniquely defined real number. Laws of Exponents If s , t , a , and b are real numbers, with 0 a > , 0 b > , then s t s t a a a + = s s t t a a a = ( ) s t st a a = 0 1 a = ( ) s s s ab a b = s s s a a b b = 1 1 s s s a a a = = The exponential function with the base a is a function of the form ( ) x f x a = , where 0 a > and 1 a . The domain of f is the set of all real numbers.
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