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,
HOME WORK