1. Another name for a logarithm
is….
Exponent
2. Which one is impossible?
a.
c.
log2 8
log2 42
b. log2 4-2
d. log2 (-8)
d. log2 (-8)
The argument can’t be negative!
3. What is the “common” base?
Base 10
4. Write as a single logarithm:
log 20 - log 2
4. Write as a single logarithm:
log 20 - log 2
𝟐𝟎
log
𝟐
Now evaluate:
10x = 10
x=1
= log 10
5. Write as a single logarithm:
log 20 + log 5
5. Write as a single logarithm:
log 20 + log 5
log 205 = log 100
Now evaluate:
10x = 100
x=2
6. Write as a single logarithm:
log4 64 - log4 16 - log4 4
6. Write as a single logarithm:
log4 64 - log4 16 - log4 4
𝟔𝟒
log4
(𝟏𝟔)(𝟒)
= log4 1
Now evaluate:
x
4
=1
x=0
7. Expand completely:
𝟒
log2
𝟑𝒙
log2 4 – log2 3 – log2 x
8. Expand completely:
𝟑𝒙𝒚𝟐
log2
𝟔
log2 3 + log2 x + 2 log2 y – log2 6
9. Rewrite as base 10 with the
change of base method
log2 9
log2 9 = x
2x = 9
log 2x = log 9
x log 2 = log 9
log 2
x=
log 2
𝒍𝒐𝒈 𝟗
𝒍𝒐𝒈 𝟐
10. Rewrite as base 10 with the
change of base method
log4 12
x=
𝒍𝒐𝒈 𝟏𝟐
𝒍𝒐𝒈 𝟒
11. Rewrite as base 10 with the
change of base method
log3 6
x=
𝒍𝒐𝒈 𝟔
𝒍𝒐𝒈 𝟑
12. Transform this function
by shifting up 2
y = log3 x
y = log3 x + 2
13. Transform this function
by shifting left 8
y = log3 x
y = log3 (x + 8)
14. Transform this function
by shifting right 2, down 4 AND
stretch vertically by 7
y = log3 x
y = 7log3 (x - 2) - 4
15. Rewrite in exponential form.
log6 36 = 2
2
6
= 36
16. Rewrite in exponential form.
log9 729 = 3
3
9
= 729
17. Rewrite in exponential form.
logc k = r
r
c
=k
18. Rewrite in logrithmic form.
5
4
= 1024
log4 1024 = 5
19. Rewrite in logrithmic form.
3
3
= 27
log3 27 = 3
20. Rewrite in logrithmic form.
m
k
=n
logk n = m
x-3 x
-2.5 ½
-2 1
-1 2
VA: x = -3
D: (-3, )
R: (-,)
y y-2
-1 -3
0 -2
1 -1
21. Graph y = log2 (x+3) - 2
x-1 x
-½ ½
0 1
1 2
y
-1
0
1
y+1
0
1
2
22. Find the solution set for this
inequality
VA: x = -1
log2 (x+1) +1 ≥ 2
Solution: [1,)
23. Solve Algebraically
log6 (2x - 4) = log6 2
2x - 4 = 2
x =3
24. Solve Algebraically
log (5x) = log 25
5x = 25
x =5
25. Solve Algebraically
log3 (2x - 4) = 2
32 = 2x - 4
13 = 2x
6.5 = x
26. Solve Algebraically
log (x + 500) = 3
103 = x + 500
500 = x
27. Solve Algebraically
103x = 50
log 50 = 3x
1.70 = 3x
.566 = x
28. Solve Algebraically
4(3)x+2 = 60
(3)x+2 = 15
log3 15 = x + 2
2.465 = x + 2
.465 = x
29. The value of your $150,000 house is increasing
by 3.5% each year. What will be the value of your
house in 10 years?
y = 150,000(1.035)10
y = $211,589.81
30. When will the value of your house be 180,000?
180,000 = 150,000(1.035)x
1.2 = (1.035)x
log1.035 1.2 = x
5.3 = x