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Solve Exponential and Logarithmic Equations

Solve Exponential and Logarithmic Equations. Lesson 7.6 Algebra II. Agenda. Schedule for this week: Monday – lesson 7.6 Tuesday – chapter review Wednesday/Thursday – 30 minute review and Chapter 7 test (7.7 not on test) Friday – Review of 1-14 on handout Today- Lesson 7.6

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Solve Exponential and Logarithmic Equations

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  1. Solve Exponential and Logarithmic Equations Lesson 7.6 Algebra II

  2. Agenda Schedule for this week: Monday – lesson 7.6 Tuesday – chapter review Wednesday/Thursday – 30 minute review and Chapter 7 test (7.7 not on test) Friday – Review of 1-14 on handout Today- Lesson 7.6 Homework: 7.6 from the assignment sheet

  3. No Books out please… please take notes.

  4. Solve Exponential and Logarithmic Equations Let’s say that we would like to solve the following equation: What would your first step be? Tell your neighbor… when you think you know put your thumb up.

  5. Solve Exponential and Logarithmic Equations The first step is to get the equations into the same base… There are a couple of ways to do this…

  6. Solve Exponential and Logarithmic Equations Could you rewrite 4 and using the base of 2?

  7. Solve Exponential and Logarithmic Equations Could you rewrite 4 using a base of ?

  8. Solve Exponential and Logarithmic Equations Either technique will work… let’s see why… Property of Equality for Exponential Equations: Algebra: If b is a positive number other than 1, then then So…

  9. Solve Exponential and Logarithmic Equations Starting with if and we can substitute both into the equation... using our properties we can say that… (remember the distributive property). From here we can say that

  10. Solve Exponential and Logarithmic Equations and

  11. Solve Exponential and Logarithmic Equations Check your answer: Original equation We found that Substitute it back into the equation

  12. Solve Exponential and Logarithmic Equations original equation and express numbers in same base substitute into equation power of a power property property of equality for expeq’n add x to both sides divide both sides by 3

  13. Solve Exponential and Logarithmic Equations • original equation • express numbers in same base • substitute into equation • Use properties of exponents • property of equality for exponential equations • Solve for x 7. Check your answer

  14. Solve Exponential and Logarithmic Equations Do these practice problems:

  15. Solve Exponential and Logarithmic Equations Sometimes it’s difficult to express things in the same base… for instance.. What would you do if you needed to solve the following equation… How could you start this problem?

  16. Solve Exponential and Logarithmic Equations How could you start this problem? Take the log of both sides: Simplify using the Power property: Solve for x: Check your answer

  17. Solve Exponential and Logarithmic Equations

  18. Solve Exponential and Logarithmic Equations • Take the log of both sides • Simplify using the properties of logs • Use algebra to solve for x • Check your answer

  19. Solve Exponential and Logarithmic Equations Try these problems:

  20. Solve Exponential and Logarithmic Equations Property of Equality for Logarithmic Equations: If b, x and y are positive numbers and then if and only if Example:

  21. Solve Exponential and Logarithmic Equations Sometimes the easiest way to solve something is by exponentiation… For instance: Always check your answers… check for extraneous roots.

  22. Solve Exponential and Logarithmic Equations Let’s try these problems….

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