1. Warm – up #4
1. Evaluate 𝑙𝑜𝑔 5 62 = 𝑙𝑜𝑔62 𝑙𝑜𝑔5 = Condense 𝑙𝑜𝑔 2 9− 𝑙𝑜𝑔 2 3 = 𝑙𝑜𝑔 = 𝑙𝑜𝑔 Expand 𝑙𝑜𝑔 5 10 (3𝑥+1) 4 = 𝑙𝑜𝑔 𝑙𝑜𝑔 5 (3𝑥+1)

2. Homework Log Thurs 2/11 Lesson 7 – 5 Learning Objective:
To solve exponential & log equations
Hw: Pg. 473 #7 – 22, Calc Ready & Decimal Answer

3. 2/11/16 Lesson 7 – 5 Exponential & Log Eq’ns Day 1
Algebra II

4. Learning Objective To solve exponential equations
To solve log equations

5. Solve
𝑥 =81
( 3 3 ) 3𝑥 = 3 4
3 9𝑥 = 3 4
9x = 4
x = 4 9
𝑥 =8 ( 2 4 ) 3𝑥 = 𝑥 = x = 3 x = 1 4

6. Solve
4. 3 𝑥 = 1 9
3 𝑥 =
3 𝑥 = 3 −2
x = – 2
= 8 𝑥 = ( 2 3 ) 𝑥 2 −2 = 2 3𝑥 – 2 = 3x x = − 2 3

7. Solve
𝑥 =32
2 5𝑥 = 2 5
5x = 5
x = 1
5. 4 2𝑥 = 32 𝑥+1 ( 2 2 ) 2𝑥 = ( 2 5 ) 𝑥+1 2 4𝑥 = 2 5𝑥+5 4x = 5x + 5 x = −5

8. Solve
𝑥 =285 𝑙𝑜𝑔 =3𝑥 𝑥= 1 3 𝑙𝑜𝑔 𝑥= 1 3 ( 𝑙𝑜𝑔285 𝑙𝑜𝑔15 ) Calculator Ready 𝑥=0.70 Solution
8. 3 𝑥 =5
𝑙𝑜𝑔 3 5=𝑥
𝑥= 𝑙𝑜𝑔5 𝑙𝑜𝑔3
Calculator Ready
𝑥=1.46
Solution

9. Solve
9. 5 2𝑥 =130 𝑙𝑜𝑔 5 130=2𝑥 𝑥= 1 2 𝑙𝑜𝑔 𝑥= 1 2 ( 𝑙𝑜𝑔130 𝑙𝑜𝑔5 ) Calculator Ready 𝑥=1.51 Solution
𝑥 −2=13
2 3𝑥 =15
𝑙𝑜𝑔 2 15=3𝑥
𝑥= 1 3 𝑙𝑜𝑔 2 15
𝑥= 1 3 ( 𝑙𝑜𝑔15 𝑙𝑜𝑔2 )
Calculator Ready
𝑥=1.3
Solution

10. Solve
𝑥= 𝑙𝑜𝑔3 𝑙𝑜𝑔
Calculator Ready
𝑥=0.84
Solution
11. 7− 5 2𝑥−1 =4 − 5 2𝑥−1 =−3 5 2𝑥−1 =3 𝑙𝑜𝑔 5 3=2𝑥−1 2𝑥= 𝑙𝑜𝑔 𝑥= 1 2 𝑙𝑜𝑔

11. Sketch a Graph 12. 𝑓(𝑥)= ( 1 2 ) 𝑥 x y – 2 – 1 1 2 ( 1 2 ) −2 = 4
12. 𝑓(𝑥)= ( 1 2 ) 𝑥
x y
– 2
– 1 1 2
( 1 2 ) −2 = 4
( 1 2 ) −1 = 2
( 1 2 ) 0 = 1
( 1 2 ) 1 = 1 2
( 1 2 ) 2 = 1 4

12. Sketch a Graph 13. 𝑓 𝑥 = 3(2) 𝑥 x y 3∙2 −2 = 0.75 – 2 3∙2 −1 = 1.5 – 1
13. 𝑓 𝑥 = 3(2) 𝑥
x y
– 2
– 1 1 2
3∙2 −2 = 0.75
3∙2 −1 = 1.5
3∙2 0 = 3
3∙2 1 = 6
3∙2 2 = 12

13. Ticket Out the Door
Solve 8 3𝑥 =154

14. Assignment: Pg. 473 #7 – 22, Calc Ready & Decimal Answer