mac1140_lecture23_1

mac1140_lecture23_1 - L23 5.3 Logarithmic Functions The...

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200 L23 §5.3 Logarithmic Functions The exponential function () x fx a = (0 , 1 ) aa >≠ is a 1-1 function and, therefore, it has the inverse 1 fx . We denote the inverse log a x and read “logarithm to the base a of x ”. Sketch the graphs of 2 x y = and 2 log yx = . Sketch the graphs of 1 2 x y ⎛⎞ = ⎜⎟ ⎝⎠ and 1 2 log =
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201 We use what we know about x ya = and inverses to get the properties of log a yx = . () x fx a = 1 () l o g a fx x = Points (0,1) and (1, ) a are on the graph Points ( , ) and ( , ) are on the graph 0 y = is HA Domain: ( , ) −∞ +∞ Domain: ( , ) Range: (0, ) +∞ Range: ( , log x a ax = for any real x log a x = for 0 x > **Important** Since inverse functions undo each other with respect to composition, the following identities hold: log for all real x a x = log for 0 a x x = > . We use these identities for solving exponential and logarithmic equations and inequalities.
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202 Logarithms and Exponents: The main property of inverses, applied to logarithms and exponents, is: log y a x y ax = ⇔= 0 a > , 1 a , 0 x > Note : exponential and logarithmic forms are convertible.
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This note was uploaded on 02/29/2012 for the course MAC 1140 taught by Professor Gregory during the Fall '11 term at Broward College.

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mac1140_lecture23_1 - L23 5.3 Logarithmic Functions The...

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