1
Algebra II – Chapter 7 Logarithm Worksheet
Name ________________________________________ Date ________
Condense the following logarithms.
#1. 5 log w + 6 log q
#2. 6 log w – 5 log y
#3. log x – 2 log w
#4. 7 log v + log x
#5. log x – (log z + log w)
#6. 6log w + 5log x + 10log y
#7. 4 log 2 + log 3
#8. 2 log 5 – log 10
#9. 3 log 3 – log x
#10. 5 log x – (2 log 6 + 9 log y)
#11. 6 log w + 8 log y – (log b + 7 log z)
#12. 5 log 2 + 2 log 6
#13. log (x + 9) + log z
#14. log (x – 8) – log 15
Expand the following logarithms.
#15. log 𝑥
#17.
log
4 7 9
𝑦 𝑧
√𝑥
𝑦6
Use the power property to simplify each:
#19. ½ log 100
#20. ½ log 81
#16.
log
𝑦8
𝑥3
#18. Log √𝑥 ∗ 𝑤 11 ∗ 𝑡17
#21. ½ log 16
#22. ½ log 49
2
#23. Consider the following function: g(x) = −𝟏𝟐 𝒍𝒐𝒈𝟕 (𝒙 + 𝟗) − 𝟏𝟎
Indicate how the basic function found in step 1 has been shifted, reflected, stretched, or
compressed.
Horizontal shift:
ᴑ LEFT
ᴑ RIGHT
ᴑ NONE
# of units: ______
Stretch/Compress:
ᴑ STRETCH
ᴑ COMPRESS
ᴑ NONE
By a factor of: _____
X-Axis Reflection:
ᴑ yes
ᴑ no
Y-Axis Reflection:
ᴑ yes
ᴑ no
Vertical Shift:
ᴑ UP
ᴑ DOWN
ᴑ NONE
# of units: ______
#24. Consider the following function:
𝟑
g(x) = − 𝒍𝒐𝒈𝟗 (𝒙 − 𝟕) + 𝟐
𝟒
Identify the more basic, parent function that has been shifted, reflected, stretched, or
compressed.
Horizontal shift:
ᴑ LEFT
ᴑ RIGHT
ᴑ NONE
# of units: ______
Stretch/Compress:
ᴑ STRETCH
ᴑ COMPRESS
ᴑ NONE
By a factor of: _____
X-Axis Reflection:
ᴑ yes
ᴑ no
Y-Axis Reflection:
ᴑ yes
ᴑ no
Vertical Shift:
ᴑ UP
ᴑ DOWN
ᴑ NONE
# of units: ______
#25. Consider the following function: g(x) = 𝟕(𝟓)𝒙+𝟗 + 𝟏𝟎
Indicate how the basic function found in step 1 has been shifted, reflected, stretched, or
compressed.
Horizontal shift:
ᴑ LEFT
ᴑ RIGHT
ᴑ NONE
# of units: ______
Stretch/Compress:
ᴑ STRETCH
ᴑ COMPRESS
ᴑ NONE
By a factor of: _____
X-Axis Reflection:
ᴑ yes
ᴑ no
Y-Axis Reflection:
ᴑ yes
ᴑ no
Vertical Shift:
ᴑ UP
ᴑ DOWN
ᴑ NONE
# of units: ______
3
Use the formula below for the next THREE questions:
𝑨(𝒕) = 𝒂(𝟏 + 𝒓)𝒕
#26. Suppose you deposit $30,000 in a savings account that pays interest at an annual rate of
5%. If no other money is added or withdrawn from the account, how much will be in the
account after 12 years?
#27. Suppose you deposit $60,000 in a savings account that pays interest at an annual rate of
2.4%. If no other money is added or withdrawn from the account, how much will be in the
account after 8 years?
#28. Suppose you purchase a new car for $40,150. If the rate of depreciation is 7.8% per year,
how much will the car be worth in 5 years?
#29. In April 2010, a town was hit by an earthquake with a magnitude of 8.4 on the Richter
scale. The same town was hit by an earthquake with a magnitude of 6.1 in June 2010. How
many times more intense was the earthquake in June than in April? Use the formula
log
I1
 M1  M 2
I2
to solve the problem.
Use the change of base formula to evaluate the following. Round all answers to the nearest
HUNDREDTH (two decimal places)
#30. 𝑙𝑜𝑔1⁄ 0.2975
#31. 𝑙𝑜𝑔1⁄ 8.075
#32. 𝑙𝑜𝑔2⁄ 0.1375
5
2
3
4
#33. Consider the following function: g(x) = −𝟓√𝒙 + 𝟗 − 𝟏𝟔
Indicate how the basic function found in step 1 has been shifted, reflected, stretched, or
compressed.
Horizontal shift:
ᴑ LEFT
ᴑ RIGHT
ᴑ NONE
# of units: ______
Stretch/Compress:
ᴑ STRETCH
ᴑ COMPRESS
ᴑ NONE
By a factor of: _____
X-Axis Reflection:
ᴑ yes
ᴑ no
Y-Axis Reflection:
ᴑ yes
ᴑ no
Vertical Shift:
ᴑ UP
ᴑ DOWN
ᴑ NONE
# of units: ______
#34. Consider the following function:
𝟓
g(x) = 𝟔 (−𝒙 − 𝟗)𝟑 − 𝟏𝟗
Identify the more basic, parent function that has been shifted, reflected, stretched, or
compressed.
Horizontal shift:
ᴑ LEFT
ᴑ RIGHT
ᴑ NONE
# of units: ______
Stretch/Compress:
ᴑ STRETCH
ᴑ COMPRESS
ᴑ NONE
By a factor of: _____
X-Axis Reflection:
ᴑ yes
ᴑ no
Y-Axis Reflection:
ᴑ yes
ᴑ no
Vertical Shift:
ᴑ UP
ᴑ DOWN
ᴑ NONE
# of units: ______
#35. Consider the following function:
𝟗
g(x) = − 𝟏𝟏 |−𝒙 + 𝟏𝟕| + 𝟓
Indicate how the basic function found in step 1 has been shifted, reflected, stretched, or
compressed.
Horizontal shift:
ᴑ LEFT
ᴑ RIGHT
ᴑ NONE
# of units: ______
Stretch/Compress:
ᴑ STRETCH
ᴑ COMPRESS
ᴑ NONE
By a factor of: _____
X-Axis Reflection:
ᴑ yes
ᴑ no
Y-Axis Reflection:
ᴑ yes
ᴑ no
Vertical Shift:
ᴑ UP
ᴑ DOWN
ᴑ NONE
# of units: ______