1. Properties of Logarithms

6. Properties of Logarithms

7. Evaluate 1. 2. 3. 4.

8. Properties of Logarithms (contd.)1. 2. 3.

9. Misconceptions log (a+b) NOT the same as log a + log b
log (a * b) NOT same as (log a)(log b)
log (a/b) NOT same as (log a)/(log b)
log (1/a) NOT same as 1/(log a)

10. Basic properties of logarithms
Fill in the missing values that make the equations below true:
(a)               
    
           
         
          
(b)             
(c)               
                 

11. Change-of-Base Formula

12. For computation we use:
For example:

13. Simplify:
Simplify:
Simplify:
Simplify:

14. Rewrite the following as the sum/difference of logarithms with
no exponents

15. Rewrite the following as the sum/difference of logarithms with
no exponents

16. Rewrite the following as the sum/difference of logarithms with
no exponents

17. Rewrite the following as the sum/difference of logarithms with
no exponents

18. Rewrite the following as the sum/difference of logarithms with
no exponents

19. Rewrite the following as the sum/difference of logarithms with
no exponents

20. Rewrite the following as the sum/difference of logarithms with
no exponents

21. Rewrite the following as a single logarithm:

22. Rewrite the following as a single logarithm:

23. Rewrite the following as a single logarithm:

24. Rewrite the following as a single logarithm:

25. Theorem

26. Solve

27. If ln 2 = a and ln 3 = b, find the following in terms of a and b: