1. Solve the equations. 3 3𝑥 = 27 2𝑥+12 16 −𝑥 = 8 2𝑥−10
Warm Up
Solve the equations.
3 3𝑥 = 27 2𝑥+12
16 −𝑥 = 8 2𝑥−10

2. 7.3 Logarithms Let’s begin this lesson with a puzzle.
See if you can figure out the pattern and answer the following questions.

3. Let’s start with a SUPER FUN puzzle!
Now see if you can fill in the blanks:
𝑝𝑜𝑤𝑒𝑟 =
𝑝𝑜𝑤𝑒𝑟 =
𝑝𝑜𝑤𝑒𝑟 =3
𝑝𝑜𝑤𝑒𝑟 =1
𝑝𝑜𝑤𝑒𝑟 =
𝑝𝑜𝑤𝑒𝑟 =2
𝑝𝑜𝑤𝑒𝑟 =4
𝑝𝑜𝑤𝑒𝑟 = 1 2
Take a guess at what these statements are saying:
𝑝𝑜𝑤𝑒𝑟 2 8 =3
𝑝𝑜𝑤𝑒𝑟 =5
𝑝𝑜𝑤𝑒𝑟 3 9 =2
𝑝𝑜𝑤𝑒𝑟 =4
𝑝𝑜𝑤𝑒𝑟 =2

4. Logarithm Overview What power of 6 equals 36?
Power,6 36=2 log,6 36=2 6^2=36

5. A logarithm is an exponent (a power). 𝑙𝑜𝑔 2 32 =5 𝑙𝑜𝑔 3 27 =3
Notation
A logarithm is an exponent (a power).
𝑙𝑜𝑔 =5
𝑙𝑜𝑔 =3
Say it: ____________________
What it means:
Say it: ____________________
What it means:

6. Inverses What are some familiar examples of inverses?
Exponentials also have an inverse function: ____________
The inverse of =398 is ________
Def: 𝑙𝑜𝑔 𝑏 𝐴=𝑥 is the inverse of 𝑏 𝑥 =𝐴

7. Switching Forms
Change between exponential and logarithmic equations…
𝟗 𝟑 =𝟕𝟐𝟗
𝒍𝒐𝒈 𝟗 𝟕𝟐𝟗 =𝟑

8. ↔ Switching Forms 𝑏 𝑥 =𝐴 𝑙𝑜𝑔 𝑏 𝐴=𝑥 𝑙𝑜𝑔 6 216=3 49 2 =7
𝑏 𝑥 =𝐴 𝑙𝑜𝑔 𝑏 𝐴=𝑥
“exponential form”
“log form”

9. Example
Write each equation in exponential form.
𝑙𝑜𝑔 4 16=2
𝑙𝑜𝑔 3 729=6
𝑙𝑜𝑔 2 64=6

10. You Try!
Write each equation in exponential form.
𝑙𝑜𝑔 3 9=2
𝑙𝑜𝑔 10 1,000=3
𝑙𝑜𝑔 5 625=4

11. Write each equation in logarithmic form. 15 3 =3375 4 1 2 =2 4 3 =64
Example
Write each equation in logarithmic form.
15 3 =3375 =2
4 3 =64

12. Write each equation in logarithmic form. 3 3 =27 125 1 3 =5 6 2 =36
You Try!
Write each equation in logarithmic form.
3 3 =27 =5
6 2 =36

13. Summary
Convert each logarithmic expression to an exponential, and convert each exponential to a logarithmic.
4 3 =64
𝑙𝑜𝑔 12 12=1
𝑙𝑜𝑔 5 25=2
6 −2 = 1 36

14. Solving Logs
To evaluate (solve) logarithms the first step is to convert your problem to an exponential!
𝑙𝑜𝑔 2 16

15. Logarithm Loop
𝑙𝑜𝑔 2 16=𝑥

16. Evaluate each expression. 𝑙𝑜𝑔 3 81 𝑙𝑜𝑔 4 8 𝑙𝑜𝑔 2 4
Examples
Evaluate each expression.
𝑙𝑜𝑔 3 81
𝑙𝑜𝑔 4 8 
𝑙𝑜𝑔 2 4

17. Evaluate each expression. 𝑙𝑜𝑔 64 4 𝑙𝑜𝑔 4 4 𝑙𝑜𝑔 125 5
Examples
Evaluate each expression.
𝑙𝑜𝑔 64 4
𝑙𝑜𝑔 4 4 
𝑙𝑜𝑔 125 5

18. Evaluate each expression. 𝑙𝑜𝑔 8 8 𝑙𝑜𝑔 5 25 𝑙𝑜𝑔 64 2
You Try!
Evaluate each expression.
𝑙𝑜𝑔 8 8  
𝑙𝑜𝑔 5 25
𝑙𝑜𝑔 64 2

19. HOMEWORK
Lesson 7.3
Pg. 472 #s 13-15, 21-23, 27-30