Logarithm Properties Lesson
Presentation
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
Standards-aligned
Ashley Knight
Used 4+ times
FREE Resource
10 Slides • 23 Questions
1
Logarithm Properties Lesson
Follows Topic 14 p.13-14, 21-23
2
What is the general form of the logarithmic function?
y = a logb(x - h) + k
3
Multiple Choice
What are the effects of changing the parameter h in the general logarithmic function?
Horizontal shift
Vertical Shift
Stretch
Compression
4
Multiple Choice
Does a change in h cause a change in the domain and range?
Yes, because the shift is left/right x-values
No, because the shift is left/right y-values
5
Discuss any changes to asymptotes as well.
The asymptote shifts in the same manner, which results in a domain change. The equation of the asymptote is x = h and the domain is all real numbers greater than h.
6
Multiple Select
What are the effects of changing the parameter a in the general logarithmic function? Select all that apply.
Horizontal shift
Vertical Shift
Stretch
Compression
Reflection
7
Multiple Choice
Does a change in a cause a change in the domain and range?
Yes
No
8
Discuss any changes to the asymptote as well.
When a is negative, there is a reflection over the x-axis. Since the range of the parent function is all real numbers, a vertical stretch, compression, or reflection does not affect it. The domain is also not affected, so the asymptote is not affected either.
9
Multiple Choice
What are the effects of changing the parameter k in the general logarithmic function?
Horizontal shift
Vertical Shift
Stretch
Compression
10
Multiple Choice
Does a change in k cause a change in the domain and range?
Yes, because the shift is up/down y -values, will change the range
No, the domain and range will remain the same
11
Why or why not? Discuss any changes to the asymptote as well.
Since the range of the parent function is all real numbers, a vertical shift does not affect it. The domain and the asymptote are also not affected.
12
p. 21
Properties of Exponents/Logs
13
Open Ended
b0 =
14
Multiple Choice
bn x bm =
bnm
bn + m
bn / m
bn - m
15
Multiple Choice
bn / bm =
bnm
bn + m
bn / m
bn - m
16
Multiple Choice
(bn)m =
bnm
bn + m
bn / m
bn - m
17
Multiple Choice
1. Rewrite the statement b0 = 1 in logarithmic form:
logb0=1
log0b =1
log10 =b
logb1 = 0
18
Summarize this logarithmic property in words.
This property says that the log of 1, in any base, is always equal to 0.
19
Multiple Choice
1. Rewrite the statement b1 = b in logarithmic form.
logbb=1
log1b = b
logb1=b
20
Multiple Choice
1. Rewrite the statement bn • bm = bn + m in logarithmic form. Let bn = p and bm = q.
logb (p •q) = logb p + logb q
logb (p + q) = logb p x logb q
logb (p + q) = logb p + logb q
logb (p x q) = logb p x logb q
21
In your own words, state the logarithmic property you discovered in the previous question.
The log of a product is equal to the sum of the logs of each factor.
22
Multiple Choice
Rewrite the statement bn /bm = bn - m in logarithmic form. Again, let bn = p and bm = q.
logb (p / q) = logb p − logb q
logb (p / q) = logb p / logb q
logb (p - q) = logb p - logb q
logb (p - q) = logb p / logb q
23
n your own words, state the logarithmic property you discovered in the previous question.
The log of a quotient is equal to the difference of the logs.
24
Multiple Choice
Rewrite the expression log(3x) as an equivalent logarithmic expression using only addition.
log 3 + log x
log 3 / log x
log 3 - log x
(log 3)(log x)
25
Multiple Choice
Rewrite the expression below as an equivalent logarithmic expression using only subtraction.
log4(10 / 4)
log410 - log4y
log4(10 - y)
26
Multiple Choice
Apply the properties of logarithms to simplify each expression for x ≥ 0.
logx(27) − logx(3) =
log x 9
log x 24
log x 30
log x 81
27
Multiple Choice
Apply the properties of logarithms to simplify each expression for x ≥ 0.
log10(2) + log10(5) =
log1010
log107
log102/5
log10 3
28
Multiple Choice
Apply the properties of logarithms to simplify each expression for x ≥ 0.
log (2 / x) + log (x / 2)
log 1
log 4x2
log 2x
log 0
29
Multiple Choice
Rewrite the statement (bn ) m = bnm in logarithmic form. Again, let bn = p and bm = q.
logb (p) m = mlogb p
logb (pm) = mlogb p
logb (p) m = plogb m
logb (m) p = mlogb p
30
In your own words, state the logarithmic property you discovered in the previous question.
The log of an exponential expression can be written as the product of the exponent and the log of the base of that exponential expression.
31
Multiple Choice
Expand the logarithm fully using the properties of logs. Express the final answer in terms of log x, and log y.
log (x3 / y2)
3log x - 2 log y
x log 3 + 2 log y
log 3 + log x + log y + log 2
3 log x + 2 log y
32
Multiple Choice
Expand the logarithm fully using the properties of logs. Express the final answer in terms of log x, and log y.
log 7x4
log7 + 4log x
7 log x + log 4
log 7 + x log 4
log 7 - 4 log x
33
Multiple Choice
Expand the logarithm fully using the properties of logs. Express the final answer in terms of log x, and log y.
log xy3
log x + 3 log y
log x + y log 3
3 log x + log y
log x - 3 log y
Logarithm Properties Lesson
Follows Topic 14 p.13-14, 21-23
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