ECON222 WEEK1 Exp-2

ECON222 WEEK1 Exp-2 - Lecture 2: Topic: Introduction...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 1 Lecture 2: Topic: Introduction Reading for this lecture H&P, Ch 4, Sect 4.2 – 4.4 Homework for Tutorial in Week 2 Ex 4.2, pp. 180, problems 1, 3, 17, 29. Ex 4.3, pp. 185-186, problems 11, 21, 25. Ex 4.4, p. 190-191, problems 1, 7. 2 Logarithmic Functions Definition The logarithm of a number, x , to a given base, b , is the exponent, y , to which the base must be raised to obtain x . That is, log b x = y if, and only if, b y = x where b > 0, b 1, x is any positive real number, y is any real number. 3 From Exponential Form to Logarithmic Form 10 2 = 100 implies log 10 100 = 2 5 2 = 25 implies log 5 25 = 2 16 1/2 = 4 implies log 16 4 = 1/2 4 From Logarithmic Form to Exponential Form log 8 1 = 0 implies 8 0 = 1 log 2 32 = 5 implies 2 5 = 32 log 3 ( 1/9 ) = -2 implies 3 -2 = 1/9 5 y = log 10 x that is, f(x) = log 10 x xy . 0.5 -0.301 1.0 0.0 1.5 0.176 2.0 0.301 10.0 1.0 100 2.0 Graphing Log Functions, b > 1 x y 1 10 0 = 1 10 1 = 10 10 2 = 100 calculator calculator calculator 6 y = log 0.1 x 0.5 0.301 1.0 0.0 1.5 -0.176 2.0 -0.301 10.0 -1.0 100 -2.0 Graphing Log Functions, 0 < b < 1 x y 1 0.1 0 = 1 0.1 -1 = 10 0.1 -2 = 100 Like slide 5 Like slide 5 See slide 5
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 Properties of Logarithms 1. log b (xy) = log b (x) + log b (y) 2. log b (x/y)= log b (x) - log b (y) 3. log b (x r ) = r.log b (x) 4. log b (1/x)= - log b (x) 5. log b (1) = 0 6. log b (b) = 1 7. log b (b
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/16/2010 for the course ECON 220 taught by Professor Drea during the Spring '10 term at Uni. West.

Page1 / 4

ECON222 WEEK1 Exp-2 - Lecture 2: Topic: Introduction...

This preview shows document pages 1 - 3. Sign up to view the full document.

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