1. 5.4 C OMMON AND N ATURAL L OGARITHMIC F UNCTIONS Quiz next class! Objectives: Evaluate common and natural logs with and without calculator Solve common and natural exponential and log equations by using an equivalent equation! Graph and identify transformations of common and natural log functions

2. B EFORE C ALCULATORS W E HAD L OGS ! Very useful for astronomy, chemistry, physics, and engineering Still important for sciences and engineering Today: Two most important types of logs Base 10 and Base e.

3. C OMMON L OGARITHMS : B ASE 10

4. L OGARITHMS ARE S PECIAL E XPONENTS E XAMPLE 1: E VALUATING C OMMON L OGARITHMS

5. E XAMPLE 2: USING E QUIVALENT S TATEMENTS Can be helpful:

6. N ATURAL L OGARITHMS : B ASE E ( INSTEAD OF BASE 10)

7. E XAMPLE 3: E VALUATING N ATURAL L OGARITHMS : L N Qu: How can we check to see if we did the calculations right?

8. E XAMPLE 4: S OLVING BY U SING AN E QUIVALENT S TATEMENT Qu: Do you see a statement?

9. G RAPHS OF L OGARITHMIC F UNCTIONS Think of all the graphs of the different exponential functions: The graphs of logarithmic functions have common characteristics also. What is the asymptote for each graph? Why is the domain of an exp. fn. the range of its corresponding log fn?

10. E XAMPLE 5: T RANSFORMING L OGARITHMIC F UNCTIONS

11. E XAMPLE 7: S OLVING L OGARITHMIC E QUATIONS G RAPHICALLY Understand the graph! What does the x and y values represent What is the input and output

12. 5.4 H MWR ; P. 361: 1,3, 7-13 ODD, 23-37 ODD, 43-49 ODD, 67 S TUDY FOR Q UIZ 5.1/5.2/5.4