Download powerpoint presentation for 7.4 File

3-1
PreparesLines
for F-LE.A.4
and

For exponential models,
Angles
Change of base formula
Holt Geometry
express as a
logarithm the solution to abct = d where
a, c, and d are number and the base b is
2, 10, or e; evaluate the logarithm using
technology.
3-1 Lines and Angles
Paper for notes
Pearson 7.4
Graphing Calc.
Holt Geometry
Name: Daisy Basset
3-1 Lines and Angles
TOPIC:
7.4
Properties of
Logarithms
Date :
Subject:
Period:
Objective:
Notes
Evaluate the
logarithm using
technology.
Holt Geometry
Key Concepts
3-1 Lines and Angles
 3 Properties
of Logarithms
Holt Geometry
3-1 Lines and Angles
More Log Properties
log b 1  0
log b b  1
log b b  x
x
Holt Geometry
1. What is the
expression
written as a
single
logarithm?
3-1 Lines and Angles
Holt Geometry
A.
log432 – log42
3-1 Lines and Angles
Use the Quotient Prop. Of Logs
m
log b m  log b n  log b
n
Same base
log432 – log42 = log 4
Holt Geometry
3-1 Lines and Angles
m
log b m  log b n  log b
n
32
log432 – log42 = log4
2
= log416
Write 16 as a power of 4 (same as base).
Holt Geometry
3-1 Lines and Angles
log416 = log4
2
4
log b b  x
x
log432 – log42 = 2
Holt Geometry
B.
6log2x + 5log2y
3-1 Lines and Angles
Use the Power Prop. Of Logs
n log b m  log b m
n
6
5
6log2x + 5log2y = log2x + log2y
Use the Product Prop. Of Logs
log b m  log b n  log b mn
Holt Geometry
and
Angles
3-1 Lines
log m  log
b
6
b
5
log2x + log2y =
n  log b mn
6
5
log2(x )(y )
Different, so can’t be simplified more
6log2x + 5log2y = log
6 5
x
y
2
Holt Geometry
C.
log45x + log43x
3-1 Lines and Angles
Use the Product Prop. Of Logs
log b m  log b n  log b mn
log45x + log43x = log
(5x)(3x)
4
Holt Geometry
= log415x
2
2. What is
the
logarithm
expanded?
3-1 Lines and Angles
Holt Geometry
3-1 Lines and Angles
4x
A. log
y
Use the Quotient
Prop. Of Logs
m
log b  log b m  log b n
n
4x
log
 log 4 x  log y
y
Holt Geometry
andProduct
Angles Prop. Of Logs
3-1 Lines
Use the
log b mn  log b m  log b n
log 4 x  log y
log 4  log x  log y
Holt Geometry
3-1 Lines and Angles
4
x
B. log 9
729
Use the Quotient
Prop. Of Logs
m
log b  log b m  log b n
n
4
x
4
log 9
 log 9 x  log 9 729
729
Holt Geometry
and Angles
3-1 Lines
Use the Power Prop. Of Logs
log b m  n  log b m
n
log 9 x  log 9 729  4 log 9 x  log 9 729
4
Write 729 as a power of 9.
 4 log 9 x  log 9 9
3
 4 log 9 x  3
Holt Geometry
3-1 Lines and Angles
Notes 7.4
Pearson 7.4
Calculator
Holt Geometry
3-1 Lines and Angles
250
C. log 3
37
Use the Quotient
Prop. Of Logs
m
log b  log b m  log b n
n
250
log 3
 log 3 250  log 3 37
37
Holt Geometry
and
Angles
3-1 Lines
log
250

log
3
3 37 
 log 3 2125  log 3 37
Use the Product Prop. Of Logs
 log 3 2  log 3 125  log 3 37
Write 125 as a power
 log 3 2  log 3 5  log 3 37
3
Holt Geometry
3-1 Lines and Angles
log 3 2  log 3 5  log 3 37
3
Use the Power Prop. Of Logs
250
log 3

37
log 3 2  3 log 3 5  log 3 37
Holt Geometry
Vocabulary
3-1 Lines and Angles
 Change of
Base Formula
Holt Geometry
3. What is
the value
of the
expression?
3-1 Lines and Angles
Holt Geometry
A.
log8127
3-1 Lines and Angles
Use a calculator & base 10
Use the Change of Base Formula
log 10 27
log 81 27 
log 10 81
Holt Geometry
3-1 Lines and Angles
Base 10 is the only base
you don’t have to write.
log 27
log 81 27 
log 81
Holt Geometry
and your
Anglescalculator.
3-1 Lines
Use
log 81 27  0.75
Holt Geometry
B.
log536
3-1 Lines and Angles
Use the Change
of Base Formula
& base 10.
log 36
log 5 36 
log 5
log 5 36  2.23
Holt Geometry
C.
log832
3-1 Lines and Angles
Use the Change
of Base Formula
& base 10.
log 32
log 8 32 
log 8
log 8 32  1.67
Holt Geometry
3-1 Lines and Angles
Summary
D
L
I
Q
Holt Geometry
Summarize/reflect
What did I do?
What did I learn?
What did I find most
interesting?
What questions do I still
have? What do I need
clarified?