6.5 - Properties of 6.5 - Properties of LogarithmsLogarithms

Objective: TSW Apply the properties of logarithms.

Properties of LogarithmsProperties of LogarithmsIf M, N, and b are positive numbers and bIf M, N, and b are positive numbers and b1, 1, thenthen

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 LogarithmsProperties of Logarithms

Power Property: log b Mp = p log

b M

Section 5.5 3

Examples: Expand the Examples: Expand the following logarithms.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 Now, condense the following logarithms into one logarithm…Use logarithms into one logarithm…Use the properties backwards.the properties backwards.

Section 5.5 5

zyx bbb 4log3log2log3 4.

Section 5.5 6

xzxy bbb 3log2

1log3log2/1 5.

Properties of LogarithmsProperties of Logarithmsb is a positive number and bb is a positive number and b11

log b 1 = 0 since b0 = 1Example: log 7 1

log b b = 1 , since b1 = bExample: log 7 7

Section 5.5 7

Properties of LogarithmsProperties of Logarithms

log b bx = x, since bx = bx

Example: log 7 72

blogbx = x , since log b x is the exponent to which b is raised to get xExample: 7log72

4log48

Section 5.5 8

Examples: Simplify the Examples: Simplify the following:following:6. log 9 1 + log 2 8

7. log 8 83 - log 3 1/9

8. 6log64 + log 4 64

9. log 6 6 - log 9 1

Section 5.5 9

Solve for x.Solve for x.

Section 5.5 10

8loglog3 33 x11.

pgs. 512-513 #’s 7-pgs. 512-513 #’s 7-25(odds), 29-25(odds), 29-49(odds)49(odds)