1. Objectives: To further understand the natural exponential e and natural logarithms. To solve equations involving e and ln. To know that e x and lnx are inverse functions

2. Laws of logs: log a + log b = log ab Example: log 3 + log 5 = log 15 log a - log b = log (a/b) Example: log 21 – log 7 = log 3 log a k = k log a Example: log 3 5 = 5 log 3

3. a y Remember y=a x x=log a y If y=e x then x=log e y or x=ln y e.g. e ln3 = ?

4. a y Remember y=a x => x=log a y If y=e x then x=log e y or x=ln y e.g. 2e -ln4 = ? e ln4 = ?

5. a y Remember y=a x => x=log a y If y=e x then x=log e y or x=ln y e.g. -ln e 4 = ? ln e 4 = ? GDC

6. a y Remember y=a x => x=log a y If y=e x then x=log e y or x=ln y e.g. lnx = 6 GDC

7. Activity Worksheet A Question 1 using GDC Q2-5 without GDC

8. Activity Worksheet A Question 1 using GDC Q2-5 without GDC

9. Activity Worksheet A Question 1 using GDC Q2-5 without GDC

10. Activity Worksheet A Question 1 using GDC Q2-5 without GDC

11. Activity Worksheet A Question 1 using GDC Q2-5 without GDC out of time

12. Activity Domino trail

13. SUMMARY is a growth function. (3 d.p.) At every point on, the gradient equals y : The inverse of is ( log with base e ) is defined for x > 0 only

14. Plenary mymaths: matching pairs

15. Homework: first two C3 lessons e x and lnx Topic test in 4 th lesson

16. plenary

19. Link to excel