1. Properties of Logarithmic Functions
Objectives:
Simplify and evaluate expressions involving logarithms
Solve equations involving logarithms

2. Properties of Logarithms
For m > 0, n > 0, b > 0, and b  1:
Product Property
logb (mn) = logb m + logb n

3. Example 1 given: log5 12  1.5440 log5 10  1.4307 log5 120 = 

4. Properties of Logarithms
For m > 0, n > 0, b > 0, and b  1:
Quotient Property
logb = logb m – logb n m n

5. Example 2 given: log5 12  1.5440 log5 10  1.4307 12 log5 1.2 = log5
 – 

6. Properties of Logarithms
For m > 0, n > 0, b > 0, and any real number p:
Power Property
logb mp = p logb m

7. Example 3 given: log5 12  1.5440 log5 10  1.4307 log5 1254
53 = 125
= 4  3
x = 3
= 12

8. Practice Write each expression as a single logarithm.
1) log2 14 – log2 7
2) log3 x + log3 4 – log3 2
3) 7 log3 y – 4 log3 x