Transcript 6.5 Properties of Logarithms

6.5 - Properties of
Logarithms
Objective: TSW Apply the properties of
logarithms.
Properties of Logarithms
If M, N, and b are positive numbers and b1, then
Product Property:
log b MN = log b M + log b N
Quotient Property:
log b M = log b M - log b N
N
Section 5.5
2
Properties of Logarithms
Power Property: log b Mp = p log b M
Section 5.5
3
Examples: Expand the following
logarithms.
1. log b 2x =
y
2.
log b 2 =
rs
3. log b x2 y3 =
Section 5.5
4
Now, condense the following logarithms
into one logarithm…Use the properties
backwards.
4. 3 log b x  2 log b y  3 log b 4 z
Section 5.5
5
5.
1
1 / 2 log b xy  3 log b z  log b 3 x
2
Section 5.5
6
Properties of Logarithms
b is a positive number and b1
log b 1 = 0 since b0 = 1
Example: log 7 1
log b b = 1 , since b1 = b
Example: log 7 7
Section 5.5
7
Properties of Logarithms
log b bx = x, since bx = bx
Example: log 7 72
logbx
b
=
x , since log b x is the exponent to
which b is raised to get x
log72
Example: 7
log48
4
Section 5.5
8
Examples: Simplify the following:
6. log 9 1 + log 2 8
7. log 8 83 - log 3 1/9
8.
log64
6
+ log 4 64
9. log 6 6 - log 9 1
Section 5.5
9
Solve for x.
11.
3 log 3 x  log 3 8
Section 5.5
10
pgs. 512-513 #’s 725(odds), 29-49(odds)