=?
C12 - 8-1 -
Evaluate. Think of what power must you raise the base to in order to equal the "thing you are logging".
log 8 = 3
log 16 =
log 9 =
log 1024 =
log 4 =
log 64 =
log 32 =
log 27 =
log 16 =
log 49 =
log
− log 16 =
log 0 =
log 3 =
log 1 =
100 =
log
log 2 =
1
log ⎯⎯⎯=
⎯⎯16
1
⎯⎯ =
4
log 8 =
⎯⎯
Evaluate. Think of what power must you raise the base to in order to equal the "thing you are logging".
log 3 =
log 2 =
log 4 =
log 5 =
log 5
log 3⎯⎯=
log
log
=
=
=
Change the base of the "thing you are logging" to be the same as the base of the log, and evaluate as above.
log 4 =
log 27 =
log 125 =
log 36 =
log 16 =
log 512 =
⎯⎯
log √5 =
1
log ⎯⎯=
6
Use your calculator to evaluate.
log 7 =
log 0.05 =
80 =
0=
log(−2) =
Evaluate
log
log
=
8
log 1 =
=
Evaluate
⎯⎯⎯
√10 =
log
log
log
=
4
=
log
=
=
1=
log 1000 =
10 000 =
Log Page 1
0.1 =
=c in Exp/Log Form HW
C12 - 8.1 Express in exponential form
log 8 = 3
log 1 = 0
log
⎯⎯
1
⎯⎯⎯ = 2
16
log 25 = 2
1
⎯⎯ = −1
2
log
log 27 = 3
log
log
1
log 2 = ⎯⎯
2
log ( + 2) =
log 9 = −2
⎯⎯
log
log 1 = 0
1000 = 3
=
log 100 = 2
2
16 = ⎯⎯
3
= log
1 = log 5
log 4 + 2 = 4
Express in logarithmic form
2 =8
5 = 25
2 = 64
10
1000 = 10
18 = 1
4
64 = 8
=
= 0.01
1
= ⎯⎯⎯
16
1
⎯⎯⎯ = 5
125
1
1
⎯⎯ = ⎯⎯⎯
5
25
4 =4
Log Page 2
8⎯⎯= 2
6
1
= ⎯⎯⎯
36
=
C12 - 8.1 - Logs Restrictions HW
log
=5
log( + 1) = 3
log (− ) = 5
log (
− 1) = 5
log ( − 2) = 5
log
=4
log (3 − ) = 5
log (
log
log 3 = 7
− 9) = 5
log ( + 3) = 5
2 log
log (2 − 3) = 5
=4
Log Page 3
log (
+ 4) = 5
2=4
C12 - 8.2 - log
= , log
=
Find x
1
= ⎯⎯
2
log ( ) = 3
log
=3
log
=2
log
log
log
= −2
log
= −2
log √⎯⎯ = 4
=0
Find x
log ( + 2) = 2
log ( − 5) = 2
log ( − 50) = 2
log (20 + ) = 2
log (
log (100 − ) = 4
log (5 + 7) = 2
log 2 = −5
log (8) = 3
log (144) = 2
log (81) = 2
log 5 = 1
log 5 = 3
log 125 = 3
1
log ⎯⎯⎯= 4
16
+ 100) = 3
Find x
log (64) = 3
Find x
1
log 9 = ⎯⎯
2
2
log 8 = ⎯⎯
3
3
log 27 = ⎯⎯
2
2
log 4 = ⎯⎯
3
27 3
log ⎯⎯⎯= ⎯⎯
8
2
64 3
log ⎯⎯⎯= ⎯⎯
27 2
Log Page 4
⎯⎯⎯ 3
log √27 = ⎯⎯
2
C12 - 8.2 - log
=
Solve
log (16) =
log 16 =
log
100 =
log (343) =
log
3=
log
1
log ⎯⎯=
⎯⎯9
8=
1
log ⎯⎯=
⎯⎯3
log
16 = 2
log
9=2
log 64 =
1
log ⎯⎯=
8
log 16 =
⎯⎯
log √⎯⎯4 =
1=2
9=2
Log Page 5
log (8) =
log 125 =
⎯⎯
log 1 =
⎯⎯
⎯⎯
log √8 =
4=2
C12 - 8.3 - Change of Base HW
June 18, 2014
7:07 PM
8
⎯⎯⎯⎯ =
2
125
⎯⎯⎯⎯⎯⎯⎯=
5
log 64
⎯⎯⎯⎯⎯⎯⎯=
4
log 125
⎯⎯⎯⎯⎯⎯⎯⎯=
5
log 27 =
log
64 =
log 81
⎯⎯⎯⎯⎯⎯⎯=
9
log 25 =
1
⎯⎯⎯⎯⎯⎯ =
log 3
Log Page 6
log 64
⎯⎯⎯⎯⎯⎯⎯=
4
log 81 =
1
⎯⎯⎯⎯⎯⎯ =
log 4
C12 - 8.4 - log
+ log
= log
−
=
⎯⎯
Simplify, express as a single log
3+
4=
log 5 + log 6 =
log 64 − log 16 =
10 −
log 20 − log 4 =
log 5 + log 3 + log 4 =
2=
log 4 + log 20 − log 10 =
log 4 + log 5 − log 10 =
5−
2−
4−
2+
5−
10 =
−
10 =
8−
2+
2+
10 =
5=
Express as an addition of logs
log(4 × 3) =
log(2 × 5 × 7)
4=
9=
25 =
10 =
15 =
21 =
30 =
36 =
20 =
Express as a subtraction of logs
10
log ⎯⎯⎯ =
3
3
log ⎯⎯ =
2
5=
log 0.1 =
0.5
Log Page 7
7=
C12 - 8.4 - log
Express in terms of
=
100
log(
) =
+ log
,
−
=
⎯⎯
,
log ⎯⎯ =
=
= log
16
log ⎯⎯⎯⎯⎯=
log
⎯⎯
√ =
log ⎯⎯⎯ =
log ⎯⎯⎯ =
log ⎯⎯⎯⎯
⎯ =
√
log ⎯⎯⎯⎯⎯=
10
⎯⎯⎯
log √
=
Log Page 8
C12 - 8.4 - log
+ log
Express in terms of
and
12 =
= log
−
=
.
36 =
48 =
120 =
9
log ⎯⎯⎯=
16
0.12 =
Simplify the expression.
log( + 1) + log 2 =
⎯⎯
√ + log
⎯⎯
=
log(
)−
log
− 2 log 8 =
log
=
log
log(
log( + 2) + log( + 3) =
Log Page 9
−
⎯⎯
√ =
+ 2 log 4 =
+ 5 + 6) − log( + 3) =
⎯⎯
C12 - 8.5 - Logs Equation HW
6=
−
3
24 =
+
3
Log Page 10
8=
2−
**C12 - 8.4 - Log = Log Equation HW
= log (3 − )
2 = log( + 1)
= log(
+
− 2)
=
+
−
3 log
+ log
= log(2 + 1)
2 = log( − 3)
log
4
=
81
=
5
3
+ log
+
3 log
256
= log 32
2
+
5 log
=
− log
log ( − 2) + log ( − 3) =
= log 32
log (6 + 1) − log ( − 1) =
log 3 = log (
= log 27
=
+ log
log (4 + 3) =
log (3 + 1) − log ( − 2) =
5
Log Page 11
(3 − 2)
− 4)
9
= log 8
12
4
**C12 - 8.4 - Log Equation HW
log
+ log
=2
log
+ log
=3
2 log
− log ( − 2) = 3
log 5 + log 2 = 3
log (
− 1) − log ( + 1) = 2
log
log
1 + log
4=2
log 2 − log ( − 2) = 1
27 − log
log
log
3=2
log (− ) + log (3 − ) = 2
log (3 − 12) − log
Log Page 12
=2
+ log
128 − log
=6
2=3
log 5 − log ( + 1) = 2
log
+ log ( + 2) = 2
**C12 - 8.4 - Log Equation HW
log (3 − 12) − log
log 2 − log ( − 2) = 1
log
log
log (
+ log ( + 1) = 1
+ log ( + 2) = 1
log (2 + 4) − log ( + 2) =
log
+ 5 + 6) − log ( + 2) = 1
log (2
=2
+ log ( − 6) = 3
log
+ log ( − 7) = 3
log
+ log ( + 4) = 5
log
+ log ( − 5) = 2
2 log ( + 2) − log ( + 2) = 1
+ 7 + 6) − log ( + 2) = 2
Log Page 13
**C12 - 8.4 - Log Equation Change Base HW
log
+ log
=3
2log
− log
=2
Log Page 14
C12 - 8.3 - Equation Change of Base HW
(log
(log
)(log 4) = 4
(log 36)(log 27) = 6
)(log 25)(log 16) = 8
Log Page 15
(log 16)(log 25) =
**C12 - Logs Factoring WS
(
2(
(
) +
) −3
) =4
=2
(
) =
(
= −1
(
Log Page 16
+4
) −9=0
) −7=
**C12 - Logs Exponent Equation HW
2
=
3
=
2
1
= ⎯⎯
4
3
4
2
=
2
=
=
2
=8
3
Log Page 17
=
1
= ⎯⎯⎯
27
**C12 - Logs Substitution HW
Log Page 18
C12 - 8.4 - Log Operation HW
Solve using your calculator or your brain.
10 =
5=
100 =
4528 =
1=
20 =
−1=
1000 =
. 01 =
85 =
0.1 =
3
0.2 =
9=
10
12345 =
2
0=
240 =
=
12 =
3=
8192 =
log 128 =
12 =
25 =
100 =
10
−
6 =
12 =
2
5 =
25 =
3
6
=
2
2
100 =
−2
=
10⎯⎯=
10 =
:
3
8
=
8
=
=
2
4
=
Remove a greatest common Factor of
2
5−
3=
7−
Log Page 19
2=
20 −
2=
C12 - 8.5 - Log Operation log
Square the base and the log and evaluate
log 4
log 9
log 125
log 49
Take the base and the log to the exponent −1
log 8 =
⎯⎯
log 9 =
⎯⎯
1
log ⎯⎯=
⎯⎯2
Cube the base and the log
log 4 =
log 4 =
Change the base to 3
log 64 =
log
8=
log √⎯⎯2 =
log
25 =
log √⎯⎯3 =
Change the base to 4
log 4 =
Log Page 20
1
log ⎯⎯=
⎯⎯4
C12 - 8.6 - Log/Delog Both Sides HW
Solve for
4=2
12 = 2
99 = 10
38 = 6
4=3
12 = 2
99 = 10
38 = 6
5=4
30 = 5
27 = 5
9 = 76
80 = 3
1080 = 2
7=2
5 = 2⎯⎯
40 = 5(3)
7⎯⎯
180 = 5⎯⎯
18 = 2⎯⎯⎯
60 = 3(2)
Log Page 21
C12 - 8.6 - Log/Delog Both Sides HW
4
= 12
80 = 2
3
=5
25 = 4(3)
25 = 3
2
126 = 3
=5
2
=8
80 = 4(2)
120 = 6(2)
62 = 5(3)
Log Page 22
C12 - 8.7 - Log Graphs HW
ℎ
=2
ℎ
log
= log
ℎ
ℎ
ℎ
ℎ
=3
log
ℎ
+1
= − log
ℎ
Log Page 23
ℎ
= log ( − 2)
= log (1 − )
ℎ
C12 - 8.4 - Find Inverse HW
Determine the inverse of the following
=8
= 10
=6 +7
=2
= log ( + 3)
=5
−5
= log
= 5 − log 2
Log Page 24
=3
= log (2 + 2)
2+
= log ( )
12 − 8.7 −
ℎ
= log
Graph the log
y = log
= log
= log (− )
= log
= − log
= log ( + 2)
= log
+1
=
= log ( − 3)
y = log
−2
= log (2 + 2)
= −3 log
= 3 log
⎯⎯
= log ( + 3) + 4
⎯⎯− 3 + 1
2
= 2 log ( − 3) + 4
Explain what each letter represents and does.
=
( − ℎ) +
:
:
ℎ:
:
Find the domain of the following.
= log
= log ( + 3)
= log(2 − )
= log(3 + 1)
= log (− )
= log ( − 1)
= log 2
= log(2 − 3)
= log(⎯⎯− 1)
3
= log
+2
= log
= − log
= log
( − 1)
= log(2 + 4)
How is the following related to
= log
+1
= log ⎯⎯
2
=
=
2
= log ⎯⎯+ 1
2
?
( − 2)
= −log
Log Page 25
= 2log
= log 2
= log (− )
= −3log (2 + 2) + 1