Download 5A.2 - Expanding Logs

Homework Check
SKILL CHECK
Day 2 – Convert Logs to
Exponentials, vice versa and
Solve using one to one property
5A.2 Expanding Logs
Daily Question:
 How do you expand
logarithms?
Properties of Logarithms
log a (uv)  log a u  log a v
Product Property
ln(uv)  ln u  ln v
u
log a  log a u  log a v
v
u
ln  ln u  ln v
v
log a u n  n log a u
ln u
n
 n ln u
Quotient Property
Power Property
Strategies when expanding logarithms
 Change radicals to rational (fraction) exponents.
 Expand the multiplication and/or division
 Move the exponent(s) LAST
Example 1: log
6
x
y
2
Expand.
2. log 3 2x
3.
3
3
log105x y
3
x
4. log 7
y
Expand.
2
5a
5. log 4 5
b
3
6.
3 x
ln
3
yz
Ex. 7
Expand.
1

2 
3x  5
(
3x

5
)
log

 log 
7
7


1
2
 log(3x  5)  log 7
1
 log(3x  5)  log 7
2
Ex. 8
Use log3 5  1.465 and log3 6  1.631
evaluate the logarithm.
6
A. log 3
5
B. log3 30
C. log3 36
log3 6  log3 5
log3  5 6
log 3 62
1.631 1.465
log3 5  log3 6
2log3 6
0.166
1.465 1.631
2 1.631
3.096
to
3.262
Classwork:Expand
3
1) log4 3xy
4x
2) ln
5
y
2 3
ln
a
b c
3)
43 y
4) log9 4 5
x z
(
)
Classwork:Expand
2 3
xy z
5) log
5
7) ln
ab
4
3
2
c d
3
6) log3
2 x- 1
8) log5
4 3
w y
12ab
3
c d
4
Homework:
HW WS 5A.2