1. Warmup Alg 2 27 Feb 2012

2. Warmup Alg 2 28 & 29 Feb 2012

3. Agenda Don't forget about resources on mrwaddell.net Assignment from last class period Sect 7.6: Solving log equations

4. Go over assignment from last class period

5. Section 7.6: solving log equations

6. Vocabulary Exponentials Logarithm log x ln x Any equation of the form y=(b) x The opposite of an exponential equation x= log b y No base? It is automatically base 10! “ln” is a shortcut way to write log e or log base e

7. Exponents First – Page 330

8. Product Property log b (mn) == log b m + log b n

9. Quotient Property log b = n m = log b n – log b m

10. Power Property log b m p = THIS IS EASILY THE MOST IMPORTANT ONE! = p log b m

11. Inverse Properties (2 of them) log b b x = x

12. Help! Where to find it.

13. Example problem 4 x = 2 x-2 The problem If the sides had the same base, we could do it! (2 2 ) x = 2 x-2 A little simplification 2 2x = 2 x-2 Equality rule! 2x = x-2 Regular algebra (find a zero) and subtract x from both sides x = -2

14. Example problem – You try 9 2x = 27 x-1 The problem If the sides had the same exponent, we could do it! (3 2 ) 2x = (3 3 ) x-1 A little simplification 3 4x = 3 3x-3 Equality rule! 4x = 3x-3 Regular algebra (find zeros and ones) x = -3

15. Another example 4 x = 11The problem Take the log base 4 of Both sides (why base 4?) log 4 4 x = log 4 11 x = log 4 11 Equality rule! x ≈ 1.73 Use calculator to find the answer. log 10 11 log 10 4 x = Here is how to do it, if you Don’t have an nSpire:

16. Another example – You Try 7 9x = 15The problem Take the log base ? of Both sides (why base ??) log 7 7 9x = log 7 15 9x = log 7 15 Equality rule! x ≈ Use calculator to find the answer. log 10 15 log 10 7 x = / 9 Here is how to do it, if you Don’t have an nSpire: x = (log 7 15) / 9

17. Using Logs to solve log 5 (4x-7) = log 5 (x+5)The problem Normal algebra from here Equality rule! Add 7, subtract x, divide By 3 (4x-7) = (x+5) 4x = x+12 3x = +12 x = 4

18. Using Logs to solve log 2 (x-6) = 5The problem Normal algebra from here USE THE DEFINITION OF A LOG! 2 5 = x – 6 32 = x – 6 38 = x

19. Complex Problem Solve for x. problem2log 7 x + log 7 2 = log 7 (5x+3) log 7 x 2 + log 7 2 = log 7 (5x+3) Power prop log 7 2x 2 = log 7 (5x+3) Product prop 2x 2 = (5x+3) 1 to 1 prop 2x 2 -5x - 3 = 0 Solve the quadratic (2x+1)(x-3) = 0 x = -1/2 and x = 3 Double check if you get 2 answers! Or graph the original to check!

20. Assignment Chapter 7.6: 6 – 11, 15 – 20, 24 – 27