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- 1. Solving Exponential Equations If two powers with the same base are equal, then their exponents must be equal. To solve using this property: Rewrite equation so the bases match. Set exponents equal to each other. Solve for x.
- 2. Examples: Solve:
- 3. Your Turn! Solve
- 4. Solving by Taking Logs If it is not easy/possible to rewrite using same bases, take the log (with base b) of both sides. Examples:
- 5. Your Turn! Solve
- 6. More Examples: Taking Logs Not all equations will be that basic! Must get the exponential part by itself, first. Then, take the log of both sides. Last, continue solving for x. Example:
- 7. Example: Solve
- 8. Your Turn! Solve
- 9. Natural Base Exp. Equations Get the exponential part alone. Take the ln of each side. Example:
- 10. Exponential Models Newton’s Law of Cooling – the temperature T of a cooling substance is modeled by where: t = time (in minutes) T0 = initial temp. of substance TR = room temp. r = cooling rate
- 11. Example: Your mom is making soup for dinner. When she takes it off the stove, it is 212ºF. The room temp. is 70ºF and the cooling rate of the soup is r = 0.046. How long will you have to wait to eat the soup at a safe temp. of 100ºF?
- 12. Solving Log Equations For two logs with the same base: Example: Solve
- 13. Your Turn! Solve
- 14. Equations with One Log “Chop off the log” and write in exponential form. Then solve for x. Example: Solve
- 15. Your Turn! Solve
- 16. Extraneous Solutions The domains of log functions are limited. This sometimes produces extraneous solutions. Always check answers in original equation. Example: Solve
- 17. Example: Solve
- 18. Your Turn! Solve

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