Warm – up #4 1. Evaluate 𝑙𝑜𝑔 5 62 = 𝑙𝑜𝑔62 𝑙𝑜𝑔5 = 2.56 2. Condense 𝑙𝑜𝑔 2 9− 𝑙𝑜𝑔 2 3 = 𝑙𝑜𝑔 2 9 3 = 𝑙𝑜𝑔 2 3 3. Expand 𝑙𝑜𝑔 5 10 (3𝑥+1) 4 = 𝑙𝑜𝑔 5 10+4 𝑙𝑜𝑔 5 (3𝑥+1)

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

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

Learning Objective To solve exponential equations To solve log equations

Solve 2. 27 3𝑥 =81 ( 3 3 ) 3𝑥 = 3 4 3 9𝑥 = 3 4 9x = 4 x = 4 9 1. 16 3𝑥 =8 ( 2 4 ) 3𝑥 = 2 3 2 12𝑥 = 2 3 12x = 3 x = 1 4

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

Solve 6. 2 5𝑥 =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

Solve 7. 15 3𝑥 =285 𝑙𝑜𝑔 15 285=3𝑥 𝑥= 1 3 𝑙𝑜𝑔 15 285 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

Solve 9. 5 2𝑥 =130 𝑙𝑜𝑔 5 130=2𝑥 𝑥= 1 2 𝑙𝑜𝑔 5 130 𝑥= 1 2 ( 𝑙𝑜𝑔130 𝑙𝑜𝑔5 ) Calculator Ready 𝑥=1.51 Solution 10. 2 3𝑥 −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

Solve 𝑥= 1 2 𝑙𝑜𝑔3 𝑙𝑜𝑔5 + 1 2 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 5 3 +1 𝑥= 1 2 𝑙𝑜𝑔 5 3 + 1 2

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

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

Ticket Out the Door Solve 8 3𝑥 =154

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