mac1147_lecture20_1_c

mac1147_lecture20_1_c - L20 Properties of Logarithms;...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
227 L20 Properties of Logarithms; Logarithmic and Exponential Equations Logarithm The definition of logarithm log a x follows from the identity (the cancellation rule): log a x ax = , 0 x > Logarithm to the base a (0 ,1 ) aa >≠ of a positive number x , log a x , is the power to which the base a must be raised to produce the number x . Example : Evaluate without a calculator. 2 log 16 = 5 1 log 5 = 1 2 log 1 = 5 1 log 125 =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
228 Example : Graph the functions: 3 () l o g 2 fx x =+ 3 o g( 2 ) x
Background image of page 2
229 Natural Logarithmic Function We denote: log ln e xx = . It is called the natural logarithm of x. Example. Graph the function () l n f = . ln(1/ ) e = ln1 = ln e = 2 e =
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
230 Example : Graph ln(2 ) yx = .
Background image of page 4
231 Properties of Logarithms For any positive numbers x , y and for any real r , p (0 p ) the following properties hold ( 0 a > , 1 a ): log ( ) log log aa a x yx y =+ log log log a x x y y ⎛⎞ =− ⎜⎟ ⎝⎠ log log r x rx = 1 log log p a a x x p =⋅ log 1 a a = log 1 0 a = Identities ( ) log x a ax = for all real x log a x = for 0 x > Change of Base Formula If a , b , x are positive with 1 a and 1 b , then
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/07/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

Page1 / 14

mac1147_lecture20_1_c - L20 Properties of Logarithms;...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online