1. Solve each equation for x. 1. 3x – 12 = 45 x = 19 2. x = 39.2 Algebra 3 Warm-Up 5.3

2. Algebra 3 Lesson 5.3 Objective: SSBAT write and evaluate logarithmic expressions. Standards: 2.1.11A

3. Review: Addition and Subtraction are opposite operations. Multiplication and Division are opposite operations. Squaring and Square Rooting are opposite operations.

4. Solve for x. 3 x = 19683  You could use guess and check or you can use logarithms.  Logarithms are the opposite of Exponential functions.

5. Logarithmic Equation  An equation of the form x = log b y  y is a positive number  Used to solve exponential equations  log b y is read as “log base b of y”

6. Exponential Form To Logarithmic Form y = b x x = log b y ** The base of the Exponent becomes the base of the Logarithm. ** The exponent is all by itself in the logarithm.

7. 1.5 3 = 125 Write each in Logarithmic Form 3 =log 5 125 2.4 5 = 1024 5 =log 4 1024 3.7 m = 2401 m = log 7 2401 4. 20736 = 12 4 4 =log 12 20736

8. 5.10 0 = 1 0 = log 10 1 6.

9. Change each to Exponential Form 1. log 5 15625 = 6 5 6 = 15625 2. log 2 128 = 7 2 7 = 128

10. Change each to Exponential Form 3. log x 2048 = 5.5 x 5.5 = 2048 4. = ½

11. Common Logarithm  A logarithm that has a base of 10  log 10 y  You can write it as log y - When there is no base shown it is base 10  log 10 15 = log 15  Common Logarithms are used to measure pH (acidity), decibels (sound), Richter Scale (earthquakes)

12. Since the Common Logarithm log 10 is used the most in real world applications it is given a key on the calculator. Evaluate each. 1. log 10 150 2. log 240 3. log -13 = 2.176 = 2.380 Undefined

13. Change of Base Property  Used to evaluate non base 10 logarithms in your calculator.  For any positive number M and b, with b ≠ 1 log b M =

14. Evaluate log 2 32 log (32) log (2) = 5

15. Evaluate each. 1. log 8 16 = 4/3 or 1.333…

16. 2. log 9 27 = 1.5 3. = -.83333

17. 4. log 4 (-600) Answer: Undefined (cannot take the log of a negative number)

18. On Your Own. 1. Change to Logarithmic Form 2. Change to Exponential Form 3. Evaluate. Show the change of base form. log 81 3 = ¼  81 1/4 = 3 log 2 8

19. Homework Worksheet 5.2