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

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

y = 2 x y = x Graphing the Logarithmic Function

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 Comparing Exponential and Logarithmic Function Graphs

Logarithms Consider 7 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 = 3 b) log 2 128=

Logarithms State in logarithmic form: a)b)

Evaluating Logarithms 1. log log log log log

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

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

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

Suggested Questions: Pages odd, 33-42, 47, 50 a, 52 a