2. Section 6.4 Properties of Logarithmic Functions Objectives:
Simplify and evaluate expressions involving logarithms.
Solve equations involving logarithms.
Standard:
N. Solve equations.

3. am • an = am+n Product Property
Product and Quotient Properties of Exponents
am • an = am+n Product Property
am/an = am-n Quotient Property
(am)n = am*n Power Property

4. Product and Quotient Properties of Logarithms
For m > 0, n > 0, b > 0, and b ≠ 1:
Product Property
logb (mn) = logb m + logb n
Quotient Property
logb (m/n) = logb m – logb n
** Just like the exponent rules!

5. A.
log2 12
= log2 (2 ● 2 ● 3)
= log2 2 + log2 2 + log2 3 ≈
≈3.5850

6. B.
log2 1.5
= log2 3/2
= log2 3 – log2 2 ≈
≈0.5850

7. C. log 2 18
D. log2 .75

8. Write each expression as a single logarithm. Then simplify, if possible.
A. log3 10 – log3 5
B. logb u + logb v – logb uw

9. C. log4 18 – log4 6
D. logb 4x - logb 3y + logb y

10. Power Property of Logarithms
For m > 0, b > 0, b ≠ 1, and any real number p:
logb mp = p logb m
Ex 3.
Evaluate log5 254
Log5 254 = 4 log5 25
= 4 ● 2
= 8

11. Power Property of Logarithms
Ex 4.
Evaluate log

12. Exponential- Logarithmic Inverse Properties:
For b > 0, b ≠1:
logb bx = x and blogbx = x for x > 0.
A. 3log34 + log5 25
B. log2 32 – 5log53

13. C.
7log711 + log381 D.
log885 +3log38

19. Homework
Integrated Algebra II- Section 6.4 Level A
Honors Algebra II- Section 6.4 Level B