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Algebra II
Unit 9
Name: __________________
Date: _________ Per: _____
Directions: Follow the directions for each task. Anything not completed is homework
(due tomorrow). Tomorrow we will begin class with an entry slip.
Task #1: Review your notes from Monday / Copy into notes if you don’t have them
II.
Logarithms vs. Exponents
a. Vocabulary
The first two (i and
i. Logarithm: If y = bx, then logby = x.
Remember “base raised to the
ii) are converting
b. Examples
answer equals the inside.”
from exponential
i. 25 = 52 => log525 = 2
form to logarithmic
3
ii. 1/8 = (1/2) => log1/21/8=3
form. The next two
iii.
log41 = 0 => 40 = 1
(iii and iv) are
converting from
iv. y = log (x – 5) => 10y = x – 5
logarithmic form to
exponential form.
10
Task #2: Write the opposite form in the space provided below.
1. log232 = 5
______________
2. 32 = 9
______________
3. log51 = 0
______________
4. x5 = (y – 2)
______________
5. log 10 = 1
______________
6. log1/2 2 = -1
______________
7. (1/4)-1 = 4
______________
8. log 0.1 = -1
______________
9. 6-2 = 1/36
______________
10. 100 = 1
______________
Task #3: Review your notes from Monday / Copy into notes if you don’t have them
c. Examples (Evaluating logarithms)
i. log816
log816 = x
Steps:
8x = 16
1. Write an equation in logarithmic
(23)x = 24
form
23x = 24
2. Convert to exponential form
3x = 4
3. Write each side using the same base
x = 4/3
4. Power Property of exponents
ii. log927
log927 = x
9x = 27
(32)x = 33
32x = 33
2x = 3
x = 3/2
(distribute)
5. Set the exponents equal to each
other
6. Solve for x.
iii. log64 1/32
log64 1/32 = x
64x = 1/32
(26)x = 2-5
26x = 2-5
6x = -5
x = -5/6
Think…
1
1
 5  25
32 2
Task #4: Evaluate each logarithm. Show all work below.
1. log48
2. log497
3. log5 (1/25)
4. log 0.01 = -2
5. log8127
6. log1/4 (1/8)
Task #5: NEW NOTES! Copy this into your notes.
III.
Expanding and Condensing Logarithms
a. Properties of logarithms
For any positive numbers, M, N, and b, b  1:
logbMN = logbM + logbN
(Product Property)
M
logb
= logbM – logbN
(Quotient Property)
N
logbMx = xlogbM
(Power Property)

b. Examples of condensing
i. log320 – log34
20
log3
4
log35
Use the quotient property. Then
simplify.
ii. 3log2x + log2y
 log2x3 + log2y
log2 (x3y)
iii. 3log 2 + log 4 – log 16
log 23 + log 4 – log 16
log 8 + log 4 – log 16
8 4
log
16
32
log
16
log 2

Use the both the power and
product properties. Always work
left to right.
Remember to simplify as much
as possible.
THINK BOX
Can you write 3log2 9– log6 9 as a single logarithm? Why or why not?
Task #6: Independent practice. Show all work below.
1. log24 + 3log29
2. log7a + log7b – 3log7c
3. 3log a – 2 log b
4. ½ log x – log y
5. 2 log3 3 + log35
6. log4 64 – log4 16
Task #7: NEW NOTES! Add this to your notes.
c. Examples of expanding
x
i. log5
Use the quotient property.
y
log5 x - log5 y

ii. log 3r4
log 3 + log r4
log 3 + 4log r
y 2
iii. ln  
3 
y2
ln 2
3
2
ln
y
– ln 32

2 ln y – 2 ln 3
Use the product and power properties.
Simplify by distributing the exponent.
Then use quotient and power properties.
Is there another way to do this one?

Task #8: Independent
practice. Show all work below.
a
1. log3
2. log (3x3y2)
b

3. log (2x)-2
4. log5
x 3 y 2
z

5. ln
ab
c 2
6. log27b

Any questions? Write them here. More practice problems on the website: sternmass.org