change & evaluate the following logarithmic equations to exponential equations
TRANSCRIPT
5
11) log
51
151
5
512) log 25 3
ChangeChange & & EvaluateEvaluate the following the following Logarithmic Equations to Exponential Logarithmic Equations to Exponential Equations.Equations.
35 125
103) log 10 1110 10
34) log1
9x
3
1
9x
45) log 64 p
4 64p
23 3x 2x
34 4p 3p
Objective: (1) Graphing Exponential Growth Functions (2) Using Exponential Growth Models.
Agenda: 03/03/15Agenda: 03/03/151.) Warm-up
2.) Questions:
WS Simplifying Logs
3.) Lesson 8.4 Continue
4.) Class/Homework
TB pg. 490: #’s 48 – 64 ALL ,65 – 76 ODD
5.) Work With Your Neighbor
STAY ON TASK!!!
8.4 Logarithmic FunctionsGoal 2: Graphing Logarithmic Functions
MORE SPECIAL LOGARITHMIC VALUES
Let b be a positive real number such that b ≠ 1.
log b b x = x
(LEARN THESE VALUES)
xb xb log
8.4 Logarithmic Functions Continued
Ex. 4 Use the special values to simplify the following expressions
1log) 7a
0
19) log 9b
1
23 3log)c
2
10log77)d
10
2log10)e
2
xf 9log) 3
x)3(log 23
x23 )3(log
x2
10) log 1000xg3
10log (10 )x
310log (10) x
x3
8.4 Logarithmic FunctionsContinued
Ex. 5 Finding INVERSES of logarithmic functions
xya 3log)
yx 3log
xy 3
xyb3
1log)
yx3
1log
x
y
3
1
xyc 7ln)
yx 7ln
yx ee 7ln
ye x 7
7
xey
)1ln() xyd
)1ln( yx
)1ln( yx ee
1ye x
1 xey
Step 1) Interchange x and Y
Step 2) Write as an Exponential Equations
8.4 Logarithmic FunctionsContinued
Graphing Logarithmic Functions
khxay b )(log
a = Initial x – intercept
b = base
• if b > 1, then graph moves up to the right
• if 0 < b < 1, then graph moves down to the right
h = horizontal shift and vertical asymptote
k = vertical shift
Domain: x > h
Range: All real numbers
8.4 Logarithmic FunctionsContinued
)(log10 xy
Ex. 6 For the following graphs give all the details and then draw the picture.
a = 1
b = 10 (b > 1, up to the right)
h = 0
k = 0
Domain: x > 0
Range: All real numbers
10log ( 0) 0y x
1 2 3 4 5 6
8.4 Logarithmic FunctionsContinued
)2(log5 xy
Ex. 7 For the following graphs give all the details and then draw the picture.
a = 1
b = 5 (b > 1, up to the right)
h = 2
k = 0
Domain: x > 2
Range: All real numbers
5log ( 2) 0y x
642 8 10 12-2
-4
-6
8.4 Logarithmic FunctionsContinued
2)1ln( xy
8. For the following graphs give all the details and then draw the picture.
a = 1b = e (b > 1, up to the right)h = - 1 k = - 2Domain: x > - 1Range: All real numbers
x – intercept: set y = 0
0 = ln(x + 1) – 2
2 = ln(x + 1)
e 2 = x + 1
6.4 ≈ x
1 2 3 4 5 6 7-1
-2
-3
8.4 Logarithmic FunctionsContinued
)2ln( xy
Ex. 9 For the following graphs give all the details and then draw the picture.
a = 1
b = e (b > 1, up to the right)
h = 2
k = 0
Domain: x > 2
Range: All real numbers
ln( 2) 0y x
642 8 10 12-2
-4
-6
8.4 Logarithmic FunctionsContinued
1log3
1 xy
Ex. 10 For the following graphs give all the details and then draw the picture.
a = 1
b = 1/3 (0<b<1, up to the left)
h = 0
k = -1
Domain: x > 0
Range: All real numbers
1
3
log ( 0) 1y x
1 2 3 4 5 6 7-1
-2
-3
HOMEWORK
Page 490: 49 – 75 ODD, 79 & 81