1. Objectives: 1.Be able to convert a logarithmic function into an exponential function. 2.Be able to convert an exponential function into a logarithmic function. 3. Be able to convert a natural log (ln) into an exponential function. 4. Be able to evaluate log functions using the same base formula. Critical Vocabulary: Logarithmic Function, Natural Log, Exponential Function

2. I. Convert from a log into exponential a. Formula: y = log a x  x = a y b. Examples 1. log a 7 = 12 Solution: 7 = a 12 2. log 4 x = 8 Solution: x = 4 8 II. Convert from an exponential into a log a. Formula: x = a y  log a x = y b. Examples 1. a 4 = 9 Solution: log a 9 = 4 2. 5 x = 12 Solution: log 5 12 = x

3. III. Natural Log into an exponential function a. Formula: y = ln x  x = e y b. Examples 1. ln 5 = x Solution: 5 = e x 2. ln x = 7 Solution: x = e 7 3. e x = 21 Solution: ln 21 = x

4. IV. Evaluating Logs a. Same base formula 1. Formula: If a u = a v, Then u = v 1. 3 x = 9 Solution: x = 2 2. log 2 4 = x Solution: x = 2 b. Examples Solution: x = -1 3 x = 3 2 2 x = 4 2 x = 2 2 3 x = 1/3 3. log 3 (1/3) = x 3 x = 3 -1

5. 4. log 8 16 Solution: x = 4/3 5. log 4 2 6. log 9 (1/3) Solution: x = -1/2 8 x = 16 2 3x = 2 4 3x = 4 4 x = 2 2 2x = 2 2x = 1Solution: x = 1/2 9 x = 1/3 3 2x = 3 -1 2x = -1 IV. Evaluating Logs

6. 7. log 1/27 9 8. Solution: x = 8 (1/27) x = 9 27 -1x = 9 3 -3x = 3 2 -3x = 2Solution: x = -2/3 IV. Evaluating Logs 8.

7. Homework: Page 503-504 #3 – 27 odds, 37-43 odds, 55, 57