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**Unformatted text preview: **y = ln F ( x ), using the Laws of Logarithms to simplify the new equation, 1 dierentiating the equation implicitly with respect to x , solving the resulting equation for y . The Laws of Logarithms : Given a > , a 6 = 1, x and y are positive numbers, then 1. log a ( xy ) = log a x + log a y 2. log a ( x y ) = log a x-log a y 3. log a ( x r ) = r log a x Example 7 of Section 3.6 (textbook): Example 8 of Section 3.6 (textbook): The Number e as a Limit In Section 3.1, we learned that: if f ( x ) = a x ( a > , a 6 = 1) then e is the number such that f (0) = lim h e h-1 h = 1. Reminder : The geometric meaning of the slopes f (0) of the exponential function f ( x ) = a x In this section, e can be rigorously dened as e = lim x (1 + x ) 1 x (check the proof on page 219 of the textbook). From the above graph and table, e 2 . 7182818. 2...

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