Download 7.6 Day 2.notebook - Moore Public Schools

7.6 Day 2.notebook
January 31, 2017
Objective
Bell Work
-------------------------
Solve for x.
1. 8x + 3 = 32x ­ 1
Students will learn why logarithms
2. 3x ­ 1 + 4 = 12
sometimes have extraneous
solutions by solving logarithmic
equations and checking their
solutions.
Jan 30­3:33 PM
7.6 Solving Logarithmic Equations
Jan 27­7:43 AM
1/31
Ex. 5: Solve log4 (5x ­ 1) = 3.
logarithmic equations: equations that involve logarithms of variable expressions
Property of Equality for Logarithmic Equations
If b, x, and y are positive numbers with b ≠ 1, then logb x = logb y if and only if x = y
Ex. 4: Solve.
a) log5 (4x ­ 7) = log5 (x + 5)
b) ln (7x ­ 4) = ln (2x + 11)
Jan 30­3:36 PM
Jan 30­3:40 PM
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7.6 Day 2.notebook
January 31, 2017
Ex. 6: What is (are) the solution(s) of log 2x + log (x ­ 5) = 2?
Wrap It Up...
1. How do you solve an exponential function?
2. How do you solve a logarithmic function?
3. What are the properties of equality?
Jan 30­3:42 PM
Jan 30­3:53 PM
Assignment: P. 520 #24­42 evens
Solve the equation. Check for extraneous solutions.
Homework Help!
34. 3*1/3 log5 12x = 2*3
38. log4 (­x) + log4 (x + 10) = 2
Product Property
log5 12x = 6
24. log5 (5x + 9) = log5 6x
26. ln (x + 19) = ln (7x ­ 8)
28. log (12x ­ 11) = log (3x + 13)
30. log6 (3x ­ 10) = log6 (14 ­ 5x)
Ex. 4
log4 (­x(x + 10)) = 2
I have log5
I need an expo. w/ base 5
Ex. 5
5log 12x = 56
Ex. 6
12x = 15625 12 12
I have log4
I need an expo. w/ base 4
5
4log (­x(x + 10x)) = 42 ­x(x + 10x) = 16
­x2 ­ 10x ­ 16 = 0
FACTOR
­(x2 + 10x + 16) = 0
­(x + 8)(x + 2) = 0
x = ­8 & x = ­2
4
x = 1302.083
32. log4 x = ­1
34. 1/3 log5 12x = 2
36. log2 (x ­ 4) = 6
38. log4 (­x) + log4 (x + 10) = 2
40. 4 ln (­x) + 3 = 12
42. log6 3x + log6 (x ­ 1) = 3
**Check**
log4 (­­8) + log4 (­8 + 10) = 2 log4 (­­2) + log4 (­2 + 10) = 2
2 = 2
2 = 2
x = ­8 is a solution
Jan 30­3:44 PM
and
x = ­2 is a solution
Jan 31­10:04 AM
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