Block 1 11.4 solve log equations.notebook
March 21, 2017
Block 1: New do now sheet
Series
Test Prep
Block 1 11.4 solve log equations.notebook
Check 11.3 March 21, 2017
Block 1 11.4 solve log equations.notebook
March 21, 2017
Block 1 11.4 solve log equations.notebook
March 21, 2017
Solve exponential equations using logs and change of base formula and solve logarithmic equations using log properties. Block 1 11.4 solve log equations.notebook
March 21, 2017
Whiteboard review
Block 1 11.4 solve log equations.notebook
March 21, 2017
Block 1 11.4 solve log equations.notebook
2x + 1
2(5) + 4 = 18
March 21, 2017
Block 1 11.4 solve log equations.notebook
March 21, 2017
Block 1 11.4 solve log equations.notebook
March 21, 2017
Block 1 11.4 solve log equations.notebook
March 21, 2017
Block 1 11.4 solve log equations.notebook
March 21, 2017
REview
solve for x:
log2 (1/4) = x
Block 1 11.4 solve log equations.notebook
March 21, 2017
expand:
4
3
log2 (x yz ) Block 1 11.4 solve log equations.notebook
March 21, 2017
condense:
6 log3 x + 5 log3 y ­ 4 log3 z
Block 1 11.4 solve log equations.notebook
March 21, 2017
pg 848
Complete 4­7. Be ready to share your answers.
Block 1 11.4 solve log equations.notebook
March 21, 2017
Block 1 11.4 solve log equations.notebook
March 21, 2017
Block 1 11.4 solve log equations.notebook
March 21, 2017
Solving Logarithmic Equations
1. Write as a single log
2. Convert to exponential form
3. solve the equation (if a quadratic set =0 and factor or quad formula)
4. Check your work
?
log2 ((­2)2 ­ 6(­2) = 4
?
log2 (16) = 4
log2 (82 ­ 6 8) = 4
log2 (16) = 4
Block 1 11.4 solve log equations.notebook
March 21, 2017
You try 2
log6 (x + x) = 1
log15 (x2 ­ 2x) = 1
1. Write as a single log
2. Convert to exponential form
3. solve the equation (if a quadratic set =0 and factor or quad formula)
4. Check your work
Block 1 11.4 solve log equations.notebook
log3 (x ­ 4) + log3 (x + 2) = 3
March 21, 2017
logarithmic equation ­ two logs
log3 (x ­ 4)(x + 2) = 3
1. Write as a single log
log3 (x2 ­ 2x ­ 8) = 3
2. Convert to exponential form
33 = x2 ­ 2x ­ 8
27 = x2 ­ 2x ­ 8
0 = x2 ­ 2x ­ 35
3. solve the equation 0 = (x ­ 7)(x + 5)
(if a quadratic set =0 and factor or quad formula)
x = 7, ­ 5
4. Check your work
­ 5 is extaneous ­ why?
hw #12: log2 x + log2 (x ­ 6) = 4
log3 (7 ­ 4)(7 + 2) = 3
log3 (3)(9) = 3
log3 (27) = 3
27 = 27
Block 1 11.4 solve log equations.notebook
hw #10: log4 (x + 3) + log4 x = 1
hw #12: log2 x + log2 (x ­ 6) = 4
March 21, 2017
Block 1 11.4 solve log equations.notebook
pg 856
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Block 1 11.4 solve log equations.notebook
pg 857
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Block 1 11.4 solve log equations.notebook
Assignment
pg 859­861 due Block 2
Log Practice worksheet
March 21, 2017
Block 1 11.4 solve log equations.notebook
March 21, 2017
page 857, #9
2 log (x + 1) = log x + log (x + 3)
log ((x + 1)2) = log (x(x + 3))
(x + 1)2 = x(x + 3)
x2 +2x + 1 = x2 + 3x
­x2 ­x2 _
_
2x + 1 = 3x
­2x
­2x
__
__
1 = x
check: 2 log (x + 1) = log x + log (x + 3)
2 log (1 + 1) = log 1 + log (1 + 3)
2 log (2) = log 1 + log (4)
log (2)2 = log (1(4))
log 4 = log 4
Block 1 11.4 solve log equations.notebook
2
hw #14: log2 3 + log2 (3x + 4) = log2 (39x) = 1
March 21, 2017
Block 1 11.4 solve log equations.notebook
March 21, 2017