1. Objectives:
Apply laws of logarithms to:
•
Simplify expressions
•
Solve equations

2. If
M and N are positive real #s and
b > 0 and ≠ 1, then:

3. Express
in terms of

4. Express
in terms of

5. Express
each in terms of log M
and log N:




6. log 45 – 2 log 3
(express as a single logarithm)
Simplify

7. Simplify

8. Simplify

9. Simplify:

10. If
f(x) = bx then f-1(x) = logb x
Therefore:
f-1(f(x)) = logb bx = x and
f(f-1(x)) = blogb x = x
This
means they “undo” each other.

11. Simplify:

12. Simplify:

13. Express
y in terms of x:

14. Express
y in terms of x:

15. Express
y in terms of x:

16. Solve:

17. Solve:

18. If
log9 5 = x and log9 4 = y, express
in terms of x and y:
log9 100
log9
36

19. If
log9 5 = x and log9 4 = y, express
in terms of x and y:
log9 3.2