1. 2.5.1 MATHPOWER TM 12, WESTERN EDITION 2.5 Chapter 2 Exponents and Logarithms

2. A logarithmic function is the inverse of an exponential function. y = 2 x 2.5.2

3. y = 2 x y = x 2.5.3 Graphing the Logarithmic Function

4. The -intercept is 1. There is no -intercept. The domain is The range is There is a horizontal asymptote at There is no -intercept. The -intercept is 1. The domain is The range is There is a vertical asymptote at. y = 2 x y = log 2 x The graph of y = 2 x has been reflected in the line of y = x, to give the graph of y = log 2 x. 2.5.4 Comparing Exponential and Logarithmic Function Graphs

5. Logarithms Consider 7 2 = 49. 2 is the exponent of the power, to which 7 is raised, to equal 49. The logarithm of 49 to the base 7 is equal to 2(log 7 49 = 2). Exponential notation Logarithmic form In general: If then State in logarithmic form: a) 6 3 = 216 b) 4 2 = 16 State in exponential form: a) log 5 125 = 3 b) log 2 128= 7 2.5.5

6. Logarithms 2.5.6 State in logarithmic form: a)b)

7. Evaluating Logarithms 1. log 2 1282. log 3 27 3. log 5 5 6 4. log 8 16 5. log 8 1 2.5.7

8. 6. log 4 (log 3 3 8 ) 7. 8. 9. Given log 16 5 = x, and log 8 4 = y, express log 2 20 in terms of x and y. 2.5.8 Evaluating Logarithms

9. Base 10 logarithms are called common logs. Using your calculator, evaluate to 3 decimal places: a) log 10 25 b) log 10 0.32 c) log 10 2 Evaluate log 2 9: Change of base formula: 2.5.9 Evaluating Base 10 Logs

10. 2.5.10 Evaluating Logs Given log 3 a = 1.43 and log 4 b = 1.86, determine log b a.

11. Suggested Questions: Pages 98-100 1-31 odd, 33-42, 47, 50 a, 52 a 2.5.11