Advanced Algebra
Chapter 8 “Exponential and Logarithmic Functions and Relations”
Date
Day #
Section
Page
Assignment
02/05
1
8.2 Solving Exponential Equations
8.3 Logarithms and Logarithmic
Functions
488
496
1, 11, 14, 32, 35, 50-53
13, 15, 19, 23, 25, 29, 33, 65, 67, 70
02/08
2
Graphing Exponential and
Logarithmic Equations
--
02/09
3
8.4 Solving Logarithmic Equations
504
02/10
4
QUIZ (8.2-8.4)
--
02/11
5
8.5 Properties of Logarithms
512
23-25, 39, 41, 69, 70, 71
02/12
6
8.5 Properties of Logarithms
512
8, 9, 11, 26, 45, 46, 47
02/16
7
8.6 Common Logs
519
17, 23, 25, 27, 33, 43, 45
8.7 Log Base e and Natural Logs
529
9, 11
Worksheet #2
9-19 (odd), 45, 48, 50, 52, 58, 59
Worksheet #4
02/17
8
8.8 Using Logarithmic and
Exponential Equations
--
Worksheet #8
02/18
9
QUIZ (8.2-8.8)
--
Review Packet
02/19
10
CHAPTER 8 REVIEW
--
Practice Test
02/22
11
TASK/N-Spire
02/23
12
CHAPTER 8 TEST
TBA
--
Cumulative Review
All assignment keys and blank copies of worksheets are posted on my website.
Assignments are subject to change.
Advanced Algebra w/ Trig
Notes 8.2
Goal: Students will be able to solve exponential equations
Exponential Function: An equation of the form y a x , where a > 0 and a 1.
There are 2 ways to solve for the exponent in an exponential function:
1. Force the bases to be equal, then if a x a y then x = y.
2. Logarithms – later this chapter
Solve.
1. 93 3x
2
3. 16 2 x1
2. 34 27 x1
1
32
2x
1
x5
5
25
4.
Advanced Algebra w/ Trig
Notes 8.3
Goal: Students will be able to convert exponential to logarithmic equations and vice versa.
Students will be able to evaluate logarithmic equations
Solve.
1. 23 x 4x2
2. 8 x2
Exponential Equations: y a x
1
16
(spoken as y = a to the x)
Logarithm: The “reverse” of an exponential expression, which helps us put really really big or small numbers on a
more human- friendly scale.
Logarithmic Equation: x log a y where a and y >0
(spoken as x = log base a of y)
Put in logarithmic form.
1. 52 25
2. 105 100,000
3. 80 1
6. log1 1 7
7. log 2
10. log 27 3
11. log 1
4. 34 81
Put in exponential form.
5. log 2 32 5
1
4
16
8. log 9 3
Evaluate.
9. log8 64
4
1
64
12. log16 2
1
2
Advanced Algebra w/ Trig
Notes Graphing
GOAL: Students will be able to graph logarithmic functions and solve logarithmic functions by rewriting as an
exponential function.
Exponential Form
y ax
Logarithmic Form
y log a x
Inverse Functions
Properties of Exponential Functions
Properties of Logarithmic Functions
Domain:
Domain:
Range:
Range:
x-intercepts:
x-intercepts:
y-intercept:
y-intercept:
Asymptotes:
Asymptotes:
Graph contains these points:_________________________
Graph contains these points: _________________________
Graph both on this:
Graph using transformations.
f ( x) ln( x 3)
f ( x ) 3x
f ( x) ln( x)
f ( x) 2 x 1
f ( x) log( x) 2
y 2 x 3
Advanced Algebra w/ Trig
Notes 8.4
Goal: Students will be able to solve logarithmic equations.
Simplify.
Solve.
1 3
7
1.
5n 4 10n
2
2 xy 24 x
2. 2 5
w
w
3
Calculate in the calculator:
log 4
log -4
log 100
log-100
log .5
What can you conclude?
Solve.
1. log3 27 y
4. log9 x 3
2. log 7
1
y
49
5. log b 64
3
2
3. log 1 27 y
3
6. log16 x
New Property: If logb x logb y , then x = y
7. log3 (3x 6) log3 (2 x 1)
8. log8 ( x 2 14) log8 (5 x)
3
2
log -.5
Advanced Algebra w/ Trig
Notes 8.5
Goal: Students will be able to solve logarithmic equations.
Properties of Logs:
1. logb m logb n logb m n
m
n
2. log b m log b n log b
3. log b m p p log b m
4. log b b 1
Rewrite the following expressions using a single logarithm.
1. log 2 x 4log 2 y
2. 3log x log 2
Solve. MUST CHECK ANSWERS!
1
3
3. log5 4 log5 x log5 36
4. 2 log 6 4 log 6 8 log 6 x
5. log3 6 log3 3 log3 x
6. log 6 ( x 2 3) log 6 ( x 1) log 6 7
Advanced Algebra w/ Trig
Notes 8.5 Day 2
Goal: Students will be able to solve logarithmic equations.
Solve.
Simplify.
1. log7 x log7 x 1 log7 12
x2 9
4
2.
3 x
8
Solve. MUST CHECK ANSWERS!
1. log 4 ( x 2) log 4 ( x 4) 2
2. log5 y 12 log5 y 12 2
3. log5 x 5 log5 x 1 log5 x 1
4. log2 x log2 x 2 1
Advanced Algebra w/ Trig
Notes 8.6 /8.7
Goal: Students will be able to evaluate common logarithmic expressions
Common Log: log10 are called common logarithms (we usually write without the 10)
Number e: an irrational number used in science and math e 2.718
Natural Log: ln, a log with number e as base (all properties of logs apply)
loge e 1 so ln e = 1
Exponential Equation: an equation with a variable in the exponent
Two ways to solve:
1. Force bases to be the same, set exponents equal
2. Take log (or natural log) of both sides
Solve the equations.
1. 4 x 24
2. 8 4e5 x
3. 7 x 2 53 x
4. 3x 4 5 x 1
Change of Base Formula: log a n
5. log 4 22
log b n ln n
log b a ln a
6. log12 95
7. log11 63
Advanced Algebra w/ Trig
Notes 8.8
Goal: Students will be able to solve real world problems using exponential and logarithmic equations.
Growth and Decay
y nekt
y – final amount
n – initial amount
k – g/d constant
t – time
Continuous Compounding
A Pe rt
A – total amount
P – initial amount
r – rate (decimal %)
t – time in years
Appreciation and Depreciation
Vn P 1 r
n
Vn - new value
P – initial value
r – rate (decimal %)
n – time in years
Solve.
1. Radioactive isotopes decay with time. In 9 years, just half of the mass of a 20-gram sample of an isotope
remains. This period of time is called the half-life of the isotope. Find the constant k for this isotope when t is
given in years.
2. Zeller Industries bought a piece of weaving equipment for $50,000. It is expected to depreciate at a steady rate
of 10% each year. When will the value have depreciated to $25,000?
3. The Saver’s Club at Citizen’s Fidelity Bank promises to double your money in 8.5 years. Assuming that the
investment is compounded continuously, what is the interest rate?
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