1. Solving Exponential Equations

2. Laws of Exponents LawGeneral ruleSpecific example Multiplication of exponents b m b n = b m + n 4 6 4 3 = 4 9 Power of exponents (b m ) n = b mn (bc) n = b n c n (4 6 ) 3 = 4 18 (4 2) 3 = 4 3 2 3 Division of exponents Exponents of zero b 0 = 1 4 0 = 1 Negative exponents and

3. One way to solve exponential equations is to use the property that if 2 powers w/ the same base are equal, then their exponents are equal. If b x = b y, then x=y Exponential Equations

4. Solve by equating exponents Check → Since they have the same bases we can set their exponents equal to each other and solve for x. + 3 +3 3x = 12 3

5. Your turn

6. Solve by equating exponents Since they do NOT have the same bases…we have to rewrite so they have common bases. Common base = 2 Check → Distribute! 4 = 2² 8 = 2³ - 3x 3x = 3

7. Your turn

8. Solve by equating exponents Common base = 2 Check → How can we make ½ a base of 2? Negative exponents!!! Distribute!

9. You Try

10. Your turn! Be sure to check your answer!!!

11. Your turn! Be sure to check your answer!!!

12. Your turn! Be sure to check your answer!!!

13. 4² ˣ = 1 Since they do NOT have the same bases…we have to rewrite so they have common bases. Common base = 4 4² ˣ = 4 ⁰ 2x = 0 x = 0 4² ⁰ = 1 4 ⁰ = 1 1 = 1 Check →

14. Practice/H.W. Solving Exponential Equations WS