USE PROPERITES OF LOGARITHMS TO REWRITE THE EXPRESSION

Write as a single logarithm in the form log k:

Problem 1 :

log 6 + log 5

Solution :

= log 6 + log 5

= log (6 × 5)

= log 30

Problem 2 :

log 10 - log 2

Solution :

= log 10 - log 2

= log (10/2)

= log 5

Problem 3 :

2 log 2 + log 3

Solution :

= 2 log 2 + log 3

= log 2² + log 3

= log 4 + log 3

= log (4 × 3)

 = log 12

Problem 4 :

log 5 - 2 log 2

Solution :

= log 5 - 2 log 2

= log 5 - log 2²

= log 5 - log 4

= log (5/4)

Problem 5 :

1/2 log 4 - log 2

Solution :

= 1/2 log 4 - log 2

= log 4^1/2 - log 2

= log 2 - log 2

= 0

Problem 6 :

log 2 + log 3 + log 5

Solution :

= log 2 + log 3 + log 5

= log (2 × 3 × 5)

= log 30

Problem 7 :

log 20 + log (0.2)

Solution :

= log 20 + log (0.2)

= log (20 × 0.2)

= log 4

= log 2²

= 2 log 2

Problem 8 :

- log 2 - log 3

Solution :

= - log 2 - log 3

= - (log 2 + log 3)

= - log (2 × 3)

= - log 6

Problem 9 :

3 log (1/8)

Solution :

= 3 log (1/8)

= 3log (1/2)³

= 3(3 log(1/2))

= 9 log(1/2)

= 9 log 2^-1

= 9(-1) log 2

= -9 log 2

Problem 10 :

4 log 2 + 3 log 5

Solution :

= 4 log 2 + 3 log 5

= log 2⁴ + log 5³

= log 16 + log 125

= log (16 × 125)

= log 2000

Problem 11 :

6 log 2 - 3 log 5

Solution :

= 6 log 2 - 3 log 5

= log 2⁶ - log 5³

= log 64 - log 125

= log (64/125)

Problem 12 :

1 + log 2

Solution :

= log 10 + log 2

= log (10 × 2)

= log 20

Problem 13 :

1 - log 2

Solution :

= log 10 - log 2

= log (10/2)

= log 5

Problem 14 :

2 - log 5

Solution :

= 2 log 10 - log 5

= log 10² - log 5

= log (100/5)

= log 20

Problem 15 :

3 + log 2 + log 7

Solution :

= 3 + log 2 + log 7

= 3 + log (2 × 7)

= 3 + log 14

= 3 log 10 + log 14

= log 10³ + log 14

= log (1000 × 14)

= log (14000)