Warm Up

Make a t-chart for the following functions 1. 3x

2. 3-x

3. 3x + 1

Warm Up

Math IV Lesson 16 Essential : How do you recognize, evaluate, and graph logarithmic functions? Standard: a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise. b. Investigate transformations of functions

Logarithmic form: logba = c Exponential form: bc = a Logarithmic function: f(x) = logax Natural logarithmic function: f(x) = ln(x)

New Vocabulary

CHANGING BETWEEN LOG FORM AND EXPONENTIAL FORM

We all know 32 = 9Now lets write it in log form…..

Solve for x (hint put in exponential form) 1. log232 = x

2. Log31 = x

3. Log42 = x

EVALUATING LOGS

1. loga1 = 0

2. Logaa = 1

3. Logaax = x

4. If logax = logay , then x = y

PROPERTIES OF LOGS

Solve for xLog2x = log23

Simplify log55x

Solve for x Log44 = x

EXAMPLES

Graph both

Y = 2x and y = log2x

GRAPHS OF LOGS AND EXPONENTIAL EQUATIONS

F(x) = logex = ln(x)

Properties of natural logs1.ln1 = 0 because e0 = 1 2.Ln (e) = 1 because e1 = e3.Lnex = x because e lnx = x4.If ln(x) = ln(y) then x = y

NATURAL LOG LN

Simplify the expressionsLn (1/e)

e ln5

4ln(1)

2ln(e)

USING PROPERTIES OF NATURAL LOGS

P2031-17 odd, 25-28,

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