1. 8.6 Solving Exponential & Logarithmic Equations
Standards 13, 14
8.6 Solving Exponential & Logarithmic Equations

2. Solve by Equating Exponents
Original Problem
Rewrite with base 2
Simplify exponents
Equate exponents
Simplify
Goal 1: Solving Exponential Functions

3. Goal 1: Solving Exponential Functions
White Boards a. b.
Goal 1: Solving Exponential Functions

4. Taking the Log of both sides
Original Problem
Take log2 of each side
Simplify
Change-of-base formula
Goal 1: Solving Exponential Functions

5. Goal 1: Solving Exponential Functions
White Boards a. b.
Goal 1: Solving Exponential Functions

6. Goal 1: Solving Exponential Functions
More complicated...
Solve by taking the log of both sides.
Original Problem
-4 from both sides
log both sides
Simplify +3
÷2; Simplify
Goal 1: Solving Exponential Functions

7. Goal 1: Solving Exponential Functions
White Boards
Solve by taking the log of both sides.
Goal 1: Solving Exponential Functions

8. Goal 2: Solving Logarithmic Functions
Solving Log Equations
Original Problem
Same bases cancel
Isolate x
Goal 2: Solving Logarithmic Functions

9. Goal 2: Solving Logarithmic Functions
White Boards
Goal 2: Solving Logarithmic Functions

10. Goal 2: Solving Logarithmic Functions
Exponentiating...
Original Problem
Exponentiate both sides
Simplify
Isolate x
Goal 2: Solving Logarithmic Functions

11. Goal 2: Solving Logarithmic Functions
White Boards a. b.
Goal 2: Solving Logarithmic Functions

12. Goal 2: Solving Logarithmic Functions
Extraneous Solutions
Goal 2: Solving Logarithmic Functions

13. Goal 2: Solving Logarithmic Functions
Solving Log Equations
Goal 2: Solving Logarithmic Functions