Download W17D2 Log Practice Warm Up 1. Expand ln 9x7 y3 2. Condense log 5

W17D2 Log Practice
Warm Up
9x7
1. Expand ln 3
y
2. Condense log 5 − 6 log x + 4 log y
1. ln 9 + 7 ln x − 3 ln y
2. log
1.
2.
3.
4.
5x6
y3
Change of base formula
Graphing Review
Pg 482 489 39 and 42
Worksheet bottom half
Change of base formula
EX 1:
ax = b
take the log of both sides
log10 ax = log10 b
x log10 a = log10 b
divide both sides by log10 a
log10 b
x=
log10 a
rewrite starting statement in log format
loga b = x
log10 b
loga b =
log10 a
EX 2:
EX 3:
EX 4:
log10 5
= 1.46
log10 3
log4 3
1
= log3 9 =
log4 9
2
64
= log2 4 = 2
log2
16
log3 5 =
vs
log2 64
= log16 64 = 3
log2 16
EX 8:
ln 2 = .69
ln 3 = 1.1
2
= ln 2 − ln 27 = .69 − 3.3 = −2.61
ln
27
EX 9:
3x − 6
1
Expand to 3 natural logs ln( √ ) = ln 3 + ln(x − 2) − ln 5
2
5
Groupwork bottom half of the worksheet
Do Regression on the calc for the lab?
Groupwork bottom half of the worksheet
Condense
CONDENSE (skip 28, 30?)
27.
log
28.
SKIP log9
3
x
log
y5
29.
30.
SKIP log6
31.
√
ln z 3 xy
32.
33.
34.
35.
36.
Expand
86
1130
4
11
7
106
324
log4 x3 y 9
5
a
log4
b6
√
log9 z xy
4
11
log2
66
√
3
log7 z xy
EXPAND
9.
1 + 6 log6 5
1
+ log4 11 + 4 log4 7
10.
2
3
11. 5 log6 c + log6 a
2
12. 10 ln 5 − 5 ln 2
18 log5 x − 6 log5 y
3
14. 3 log4 7 + log4 2
2
15. log2 y + log2 v + 2 log2 w
13.
16.
18 log9 12 + log9 7
3
17. 5 log9 c + log9 a
2
Inquiry Worksheet Bottom Half Answers
1.
2 log2 5 = 4.644
2.
2 log 6 = 5.17
3.
log2 5 + log2 6 = 4.907
4.
log2 53 · 6 = 9.551
5.
log2 62 · 5 = 7.492
6.
log2 5 · 23 = 5.322
7.
log2 5 + 3
8.
log4 3 + 2
9.
log5 2 + 2
10.
log3 2 + log3 x
11.
log5 7 + 2 log5 a
12.
log10 3 + log10 5 + 3 log10 x + 4 log10 y
13.
log10 3
14.
log10 30
15.
log2 x
16.
log10
x
y
17.
log2
18.
log4
1
81x2
8x3
y2
19.
log7 (7x + 3) = log7 (5x + 9)
20.
log3 (x2 + x − 6) = log3 14
x=3
x=4
21.
log2 (3x + 11) = 5
22.
log(4x − 8) = 3
x=7
x = 252
23.
log3 (6x + 3) + log2 8 = log2 128
24.
log4 64 − log4 (x − 12) = log2 8
x = 13
x = 13
25.
log5 (x2 + 3x) = log5 (−8 − 3x)
26.
4 log3 (−9x) = 4
x = −4
x=−
27.
log3
28.
− 2 log5 (x + 1) = −8
x=0
x = 624
29.
log4 3x + 2 log3 9 = log4 256
30.
log4 (x2 − 6x) = log4 (10 + 3x)
x=
1
+ log9 (x + 1) = −6 + log6 36
81
Exit Pass
1. Expand the expression and simplify log2 (32)x
2. Condense the expression and simplify log3 54 − log3 2
1. Rewrite in condensed form and simplify 2 log4 y − 2 log4 3
1
x = 12
2. Solve 2log 6 = log 27 = log x
3
log3 27 + log3 2 − log3 2 = 3
1
3
1
3
x = −1, 10