S5_Unit_3_Outcome_3 - Higher Unit 3 Higher Outcome 3...

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www.mathsrevision.com Higher Outcome 3 Higher Unit 3 Higher Unit 3 www.mathsrevision.com www.mathsrevision.com Special “e” and Links between Log and Exp Rules for Logs Exam Type Questions Solving Exponential Equations Harder Exponential & Log Graphs
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www.mathsrevision.com Higher Outcome 3 Functions Exponential Graph Logarithmic Graph y x y x (0,1) (1,0)
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www.mathsrevision.com Higher Outcome 3 The letter  e  represents the value  2.718…. .                 (a never  ending decimal).                                                     This  number occurs often in nature f(x) = 2.718. . x  = e x                                                           is called  the exponential function to the base  e . A Special Exponential Function – the  “Number”  e
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www.mathsrevision.com Higher Outcome 3 y x ( ) 2 x f x = 1 ( ) f x - = (0,1) (1,0) In  Unit 1   we found that  the exponential function  has an inverse function,  called the logarithmic  function. log 1 0 log 1 log a a x a a y a x y = = = = 2 log x The log function is the inverse of the exponential function, so it  undoes ’ the exponential function: Linking the Exponential          and the  Logarithmic Function
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www.mathsrevision.com Higher Outcome 3 f (x )  = 2 x             as k your s e lf :  2   2 1  = 2   s o   lo g 2 2  = 1  “2  t o  wh at  po we r  g ive s  2 ? ”  2   4   2 2  = 4   s o   lo g 2 4  =   “2  t o  wh at  po we r  g ive s  4 ? ”  3   8   2 3  = 8   s o   lo g 2 8  =   “2  t o  wh at  po we r  g ive s  8 ? ”  4   16   2 4  = 16   s o   lo g 2 16  =   “2  t o  wh at  po we r  g ive s  16 ?”  f (x )  = log 2 x   2 3 4 Linking the Exponential          and the  Logarithmic Function
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www.mathsrevision.com Higher Outcome 3 f (x )  = 2 x             as k your s e lf :  2   2 1  = 2   s o   log 2 2  = 1  “2  t o  what  powe r  give s  2 ? ”  2   4   2 2  = 4   s o   log 2 4  =   “2  t o  what  powe r  give s  4 ? ”  3   8   2 3  = 8   s o   log 2 8  =   “2  t o  what  powe r  give s  8 ? ”  4   16   2 4  = 16   s o   log 2 16  =   “2  t o  what  powe r  give s  16 ? ”  f (x )  = log 2 x   2 3 4 Examples (a) log 3 81 =  “    to what power gives       ?” (b) log 4 2 =  “    to what power gives       ?” 1 27 (c) log 3                = “    to what power gives        ?” 4 3 81 4 2 -3 3 Linking the Exponential          and the  Logarithmic Function 1 2 1 27
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www.mathsrevision.com Higher Outcome 3 log log
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This note was uploaded on 02/13/2012 for the course MAT 205 math 205 taught by Professor Google during the Spring '10 term at University of Phoenix.

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S5_Unit_3_Outcome_3 - Higher Unit 3 Higher Outcome 3...

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