PP Section 5.3 - LogarithmicFunctions Definition The...

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Logarithmic Functions
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Definition The logarithm function to the base a , where a > 0 and a 1, is denoted by y x a = log (read as “ y is the logarithm to the base a of x ”) and is defined by y x x a a y = = log if and only if
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x x y y = = 3 to equivalent is log 3 27 log 3 then , 27 3 Since 3 3 = = Example 9 1 3 9 1 2 log 2 then , 3 Since = - = - So the logarithm base  b  of a number  is the exponent  to which we have to raise  b  to get  a .
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Comment Notice that the logarithm to the base a of x is basically the inverse function of x a x f = ) ( x y a x a y a y x log = = = Evaluate: log 4 64 y = log 4 64 3 64 4 = = y y 3 64 log 4 =
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The graph of a log function can be obtained using the graph of the corresponding exponential function. The graphs of inverse functions are symmetric about y = x. Graph of the Logarithmic  Functions 1 , = a a y x 1 , log = a x y a
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(0, : Intercepts 0 y : Asymptote ) (0, : Range ) , (- : Domain : = = x
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This note was uploaded on 01/22/2011 for the course MATH 2 taught by Professor Gardner during the Fall '08 term at Irvine Valley College.

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PP Section 5.3 - LogarithmicFunctions Definition The...

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