1. Section 6.4* General Log. and Exponential Functions
MAT 1235 Calculus II
Section 6.4*
General Log. and Exponential Functions

2. Homework and …
WebAssign HW 6.4*

3. Preview

4. Recall Under our construction, “functions” such as
is undefined at this point.
We would like to define functions such as
so that it is defined for even irrational numbers

5. Preview Define general exp. and log. function
We are going to extend the property of ln⁡(𝑥)
to all real numbers 𝑟
(Since 2016) We may skip some of the stories to save time.

6. 6.3* 𝑎>0 Property of Inverse Function

7. So,…

8. It makes sense to define…
Exp. Function with Base 𝑎>0

9. Extended Property of ln⁡(𝑥)

10. Extended Property of ln⁡(𝑥)

11. Law of Exponents

12. Law of Exponents

13. Derivatives and Antiderivatives

14. 𝑎 𝑥 Vs 𝑒 𝑥

15. Derivatives and Antiderivatives

16. Example 1

17. Example 1

18. Example 2

19. Example 3

20. Example 3

21. Definition: Log. Function with Base a

22. Derivatives

23. log 𝑎 𝑥 Vs ln𝑥

24. Example 4

25. No Classwork…
Y needs to talk about something before the quiz