Post on 20-Jan-2016
transcript
Warm-upWarm-up 1. Convert the following log & exponential 1. Convert the following log & exponential
equationsequations Log equationLog equation Exponential Exponential
EquationEquation LogLog2 2 16 = 416 = 4 ?? LogLog3 3 1= 01= 0 ?? ?? 5522 = 25 = 25 2. Solve these log expressions:2. Solve these log expressions: LogLog226464 loglog9999 loglog33(1/9)(1/9)
3. Graph this function: f(x) = log3. Graph this function: f(x) = log33(x – 2)(x – 2)
Warm-upWarm-up 1. Convert the following log & 1. Convert the following log &
exponential equationsexponential equations Log equationLog equation Exponential Exponential
EquationEquation LogLog2 2 16 = 416 = 4
LogLog3 3 1 = 01 = 0
?? 5522 = 25 = 25
1624
130
225log5
Warm-upWarm-up 2. Solve these log expressions:2. Solve these log expressions:
LogLog226464
loglog9999
loglog33(1/9)(1/9)
6
1
2
Property of Exponential Property of Exponential EqualityEquality
xxmm = x = xnn ; if and only if m = n ; if and only if m = n
You will use this property a lot when You will use this property a lot when trying to simplify.trying to simplify.
Example 1: Solve Example 1: Solve
64 = 264 = 23n+13n+1
We want the same base (2). Can we write We want the same base (2). Can we write 64 as 264 as 2??
64 = 2x2x2x2x2x2 = 264 = 2x2x2x2x2x2 = 266
2266 = 2 = 23n+13n+1
6 = 3n + 16 = 3n + 1 3n = 53n = 5 n = 5/3n = 5/3
Example 2: Solve Example 2: Solve
55n-3n-3 = 1/25 = 1/25 We want the same base (5). Can we write We want the same base (5). Can we write
1/25 as 51/25 as 5??
25 = 5x5 = 525 = 5x5 = 522
1/25 = 1/51/25 = 1/522 = 5 = 5-2-2
55n-3n-3 = 5 = 5-2-2
n – 3 = -2n – 3 = -2 n = 1n = 1
Using Log Properties to Using Log Properties to Solve EquationsSolve Equations
Section 3-3Section 3-3
Pg 239-245Pg 239-245
ObjectivesObjectives
I can solve equations involving log I can solve equations involving log propertiesproperties
3 Main Properties3 Main Properties
Product PropertyProduct Property Quotient PropertyQuotient Property Power PropertyPower Property
Product Property of Product Property of LogarithmsLogarithms
nmmn bbb logloglog
Example Working Example Working BackwardsBackwards
Solve the following for “x”Solve the following for “x” loglog44 2 + log 2 + log44 6 = log 6 = log44 x x loglog44 2 2•6 = log•6 = log44 x x 2•6 = x2•6 = x x = 12x = 12
Product PropertyProduct Property
1)3log(log zz x333 log7log2log
1)3(log zz
10)3( zz
01032 zz
0)2)(5( zz2,5z
x33 log14log
x14
Quotient Property of LogsQuotient Property of Logs
nmn
mbbb logloglog
Working BackwardsWorking Backwards
LogLog33 6 - Log 6 - Log33 12 12 LogLog33 6/12 6/12 LogLog33 1/2 1/2
Condensing an expressionCondensing an expression
Quotient PropertyQuotient Property8log)3(log4log 222 x 2log)12log()3log( xx
8log3
4log 22
x
83
4
x
)3(84 x
2484 x
x2
5
2log12
)3(log
x
x
212
)3(
x
x
1223 xx
243 xx
x3
5
Quotient Property Quotient Property BackwardsBackwards
Solve the following for xSolve the following for x loglog55 42 – log 42 – log55 6 = log 6 = log55 x x loglog55 42/6 = log 42/6 = log55 x x x = 42/6x = 42/6 x = 7x = 7
Power Property of LogsPower Property of Logs
mpm bp
b loglog
Example Power PropertyExample Power Property
4 log4 log55 x = log x = log55 16 16 loglog55 x x44 = log = log55 16 16 xx44 = 16 = 16 xx44 = 2 = 244
x = 2x = 2
Power PropertyPower Property3
5 25log 83 27log
25log3 5
23
6
27log8 3
38
24
PracticePractice
125log3
1log 55 m
3
1
55 125loglog m
5loglog 55 m
1m
PracticePractice
x5log5log5
16log48log 6666
x5log5log
51648
log 666
x5log5log15log 666 x5log515log 66 x5log75log 66
x575
x15
PracticePractice
49log2
116log
4
1log y
2
1
4
1
49log16loglog y
7log2loglog y
14loglog y
14y
PracticePractice16log4loglog3 555 x
16log4loglog 553
5 x
16log4
log 5
3
5 x
16log4
log 5
3
5 x
164
3
x
643 x
4x
PracticePractice
2)21log(log aa2)21(log aa
100212 aa
0100212 aa
0)4)(25( aa
4,25a
PracticePractice
22log)2(log 62
6 b
22)2(log 26 b
3642 2 b
162 b4b
4b
PracticePractice0)1(log)55(log 2
33 zz
01
)55(log
23
z
z
11
)55(2
z
z
155 2 zz
650 2 zz
160 zz
1,6 z
HomeworkHomework
WS 6-3WS 6-3