1. Warm Up Solve for x: 𝟑+𝟐∙ 𝟒 𝒙 =𝟐𝟓 𝒍𝒐𝒈 𝟔 𝟑𝒙−𝟐 +𝟏=𝟏
I can solve exponential equations using properties of logarithms
Warm Up
Solve for x:
𝟑+𝟐∙ 𝟒 𝒙 =𝟐𝟓
𝒍𝒐𝒈 𝟔 𝟑𝒙−𝟐 +𝟏=𝟏
Condense or Expand using log properties
𝒍𝒐𝒈 𝟒 𝒙−𝟏 − 𝒍𝒐𝒈 𝟒 𝒙
𝒍𝒐𝒈 𝟐 𝟓 𝒙 𝟑 𝒚 𝟐

2. Warm Up
Solve for x:
𝟑+𝟐∙ 𝟒 𝒙 =𝟐𝟓

3. Warm Up
Solve for x:
𝒍𝒐𝒈 𝟔 𝟑𝒙−𝟐 +𝟏=𝟏

4. Warm Up Condense or Expand using log properties 𝒍𝒐𝒈 𝟒 𝒙−𝟏 − 𝒍𝒐𝒈 𝟒 𝒙
𝒍𝒐𝒈 𝟒 𝒙−𝟏 − 𝒍𝒐𝒈 𝟒 𝒙
𝒍𝒐𝒈 𝟐 𝟓 𝒙 𝟑 𝒚 𝟐

5. Homework Questions

6. Natural Log
What is the approximate value of 𝜋? What is the approximate value of e? In math, e is known as Euler’s number. It has an approximate value of 𝑙𝑜𝑔 𝑒 is known as the “natural log” which is represented 𝑙𝑛

7. Natural Log
Examples:
𝑙𝑛10=
ln 𝑥 =4
𝑒 2𝑥−1 =12

8. 𝑥=28 𝑥=9 𝑥=4 𝑥=45.25 𝑥=2 Practice 𝑙𝑜𝑔 5 5𝑥−15 =3 2 𝑙𝑜𝑔 3 𝑥=4
Solve each equation for x. Note: you may need to condense first!
𝑙𝑜𝑔 5 5𝑥−15 =3
2 𝑙𝑜𝑔 3 𝑥=4
𝑙𝑜𝑔 2 4𝑥−12 −3=−1
𝑙𝑜𝑔 8 𝑥+ 𝑙𝑜𝑔 8 2𝑥 =4
𝑙𝑜𝑔 7 4𝑥+90 − 𝑙𝑜𝑔 7 𝑥=2
𝑥=28
𝑥=9
𝑥=4
𝑥=45.25
𝑥=2

9. Randomly put #1 – 16 on your board Show all work to get credit 
Mark off # FREE SPACE!!!
Show all work to get credit 

10. Solve for x 𝑥 2 −5𝑥−6=0

11. Evaluate the function: If 𝑔 𝑥 = 𝑥 3 +5 𝑥 2 , find 𝑔(4𝑥)

12. Solve for x 6 7𝑥 2 +1 = 492 5

13. Solve for x. Round to the nearest thousandth. 20 𝑥 −8=−1.9

14. Find the inverse function: 𝑓 𝑥 =3+ 𝑥 3

15. Solve for x −1−26𝑥 −4=1

16. Solve for x 1 3𝑥 = 3 𝑥 + 1 3

17. Solve for x − 𝑥−1 +6𝑥=−11+3𝑥

18. Solve for x 2 𝑥 =9

19. Solve the system 𝑦=5𝑥+1 2𝑥−4𝑦=−22

20. Solve for x − 𝑥 2 =−10𝑥−4 𝑥 2 +8

21. Solve the system −𝑥−2𝑦=0 𝑦=−2

22. Evaluate the function:
If 𝑓 𝑥 = 𝑥 2 +2𝑥, find 𝑓(3+𝑥)

23. Solve for x. Round to the nearest thousandth. 10 7𝑥 +1=5

24. Find the inverse function: 𝑓 𝑥 = −6+ 3 4𝑥 2

25. Homework
Textbook
7-120, 7-132, 7-134,
7-136, and