Name_________________________________________
Pre-Calculus Honors
4.3 Evaluate Logarithms
Ms. Hindal
Unit 4 Day 3
Do Now:
1. Solve: x3 = 216
a.
2. What type of function is y = 3 * x4? What type of
function is y = 3 * 4x?
b.
c.
3. Objective 4.1: I think that the number of celebrities in
Charlotte can be modeled by the equation g(t) = 100 *
(1.04)t where t is the number of days after today.
According to the model, how many celebrities
are there in Charlotte today?
Is the population of celebrities increasing or
decreasing?
By what percent?
4. Objective 4.1: A party is ending, and as it ends, 4% of
the people still at the party leave each minute. Write a
function to model the number of people left at the party
at time t if at time 0, there were 75 people.
Act 1: What is a logarithm?
Look at the following examples of the logarithm function and it’s result. What does a logarithm do?? Fill in the blanks!
1.
2.
3.
log5 25 = 2
log9 81 = 2
log4 16 = 2
4.
5.
6.
log6 36 = ________
log7 _________ = 2
log10 1000 = 3
7.
8.
9.
log3 27 = 3
log2 32 = 5
log4 64 = ________
10. log3 81 = ________
11. log7 72 = ________
12. log13 1317 = ________
10. In words (you can get a ticket for a good explanation), what is the best way you can describe what a logarithm
equals/tells you?
“The logarithm equals the ___________________”
Act 2: Why logarithms?
You are researchers doing a long-term study. From other studies, you know that during long-term studies, some percent of
the participants decide each year that they no longer want to participate. You have 1000 participants to begin with and
each year, you think the number of people who will continue to participate will decrease by 20%. How many years
(exactly) can the study go on if you want to make sure that there are always at least 100 people in the study?
f(x) = bx
A logarithmic function is the _________________________ of an exponential function
f-1(y) = logb y
x2 = y
They _________________ each other!
3x = 120
log5 x = 3
y = bx  __________________
“The base equals the base, the logarithm equals the ___________________”
Act 3: Rearranging equations
Rewrite the exponential equations as logarithmic equations and vice versa:
1.
43 = 64
2.
2x = 7.2
4.
log4x = 5
6.
log 1000 = x
3.
102 = 100
5.
log216 = x
7.
ln x = 10
Special Characters:
Common Logarithms: logarithms with base 10
Note: Anytime you see a log without a base, it is always a
common log.
Name_________________________________________
e is an irrational number, e ≈ 2.71…
Natural logarithms: logarithms used with base e.
–Uses the abbreviation “ln”
–Note: anytime you see “ln” it is always base e.
Bingo Board Problems
Rearrange the following exponential equations as logarithmic equations:
1. 105 = 100000
6. 42 = 16
2. x3 = 2.1
7. a2 = 1.6
3
3. 2x = 7.2
1 
8


2
4.
5. ex = 5
8. 3x = 4.6
1
9. 10-1 = 10
1
10. e3x = 2

Rearrange the following logarithmic equations as exponential equations:
11. log28 = 3
12. loga3 = 6
13. log32 = x
14. log2x = 1.3
1
16. log2 4 = -2
17. logx4 = 2
 Act 4: Solving Equations
1. logx36 = 2
18. log 1000 = x
2. log5(x + 20) = 3
19.
log  x 

15. ln 7 = x
1
2
20. ln x = 4
3. log327 = x
Bingo Board Problems
1. log3x = 2
2. log5x = 3
3. log2(2x+1)=3
4. log3(3x-2) = 2
5. logx4 = 2
1 
6. logx 8 = 3
8. log5625 = x
9. ln ex = 5
10. ln e-2x = 8
7. log464 = x

11. log3243 = 2x + 1
12. log636 = 5x+3
1
14. e-2x = 3
13. e3x = 10

Act 5: Change of Base
For positive real numbers a, b, and x with a ≠ 1 and b ≠ 1: logbx = logax / logab
Example: log47 = log 7 / log 4
Solve for x:
1. log27 = x
3.
log220 = x
5.
2x = 5
2.
4.
0.5x = 12
6.
1000 * .8x = 100
8x = 175
Name_________________________________________
Homework: Pick 3 from each of the sections below:
Fill in the blank:
1. log3 9 = ________
2. log8 64 = ________
3. log2 16 = ________
4. log2 _______ = 3
Rearrange the following exponential equations as logarithmic equations:
1. 9 = 32
2. 1.12 = x
3. ex = 8
4. 1.06x = 2
Rearrange the following logarithmic equations as exponential equations:
5. log100.01 = -2
6. ln x = -1
7. log x=4
8. logx10 = 3
9. ln 4 = x
10.
log 3
1 
 2
9 

Solve for x:
11. log5x = 2
12. log2(x – 2) = 4
13. logx32 = 2
14. log381 = x
15. log416 = x – 1
Name_________________________________________