1. 4 minutes
Warm-Up
Solve each equation for x. Round your answers to the nearest hundredth.
1) 10x = 1.498
2) 10x =
Find the value of x in each equation.
3) x = log4 1
4) ½ = log9 x

2. 6.4.1 Properties of Logarithmic Functions
Objectives:
Simplify and evaluate expressions involving logarithms
Solve equations involving logarithms

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

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

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

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

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

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

9. 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

10. Homework
p.382 #13-21 odds,31,35

11. 4 minutes
Warm-Up
Write each expression as a single logarithm. Then simplify, if possible.
1) log6 6 + log6 30 – log6 5
2) log6 5x + 3(log6 x – log6 y)

12. 6.4.2 Properties of Logarithmic Functions
Objectives:
Simplify and evaluate expressions involving logarithms
Solve equations involving logarithms

13. Properties of Logarithms
For b > 0 and b  1:
Exponential-Logarithmic Inverse Property
logb bx = x
and b logbx = x for x > 0

14. Example 1
Evaluate each expression. a) b)

15. Practice Evaluate each expression. 1) 7log711 – log3 81

16. Properties of Logarithms
For b > 0 and b  1:
One-to-One Property of Logarithms
If logb x = logb y, then x = y

17. Example 2 Solve log2(2x2 + 8x – 11) = log2(2x + 9) for x.
2x2 + 8x – 11 = 2x + 9
2x2 + 6x – 20 = 0
2(x2 + 3x – 10) = 0
2(x – 2)(x + 5) = 0
x = -5,2
Check:
log2(2x2 + 8x – 11) = log2(2x + 9)
log2 (–1) = log2 (-1)
undefined
log2 13 = log2 13
true

18. Practice Solve for x. 1) log5 (3x2 – 1) = log5 2x
2) logb (x2 – 2) + 2 logb 6 = logb 6x

19. Homework
p.382 #29,33,37,43,47,49,51,57,59,61