LOGARITHMS 8

Evaluate Log0.2 – Log0.0016+ Log800.

Solution

= Log0.2 – Log0.0016+ Log800.

= Log(0.2 x 800)

            0.0016

= Log (160)   

          0.0016

= Log(1600000)

              16

= Log₁₀100,000

= Log₁₀10⁵

            

= 5Log₁₀10

= 5 x 1

= 5

∴ Log0.2 – Log0.0016+ Log800 = 5

TRY THIS……………………….

Evaluate Log2.5 – Log0.75 + Log3000.

FACTORIZATION 9

Factorize m²n² - c²

Solution

We use difference of two squares a² – b² = (a - b)(a + b)

m²n² - c² = (mn)² - (c)²

              = (mn - c)( mn + c)

Hence m²n² - c² = (mn - c)( mn + c)

TRY THIS…………….

Factorize e²n² - c²

RADICALS 4

LOGARITHMS 7

Evaluate log₂1024⁸

Solution

= log₂1024⁸

= log₂(2¹⁰)⁸

= log₂2⁸⁰

= 80 x log₂2    [since log_aa = 1]

= 80 x 1

= 80

Hence log₂1024⁸ = 80

TRY THIS.....

Evaluate log₂32²⁰

GEOMETRY 3

A regular polygon has 33 sides. Find the total angles of that polygon.

Solution

n = 33

Total angles = (n - 2)180⁰

                   = (33 – 2)180⁰

                   = 31 x 180⁰

                   = 5580⁰

Total angles = 5580⁰

TRY THIS……………………….

A regular polygon has 24 sides. Find the total angles of that polygon.

DISTANCE 1

FACTORIZATION 8

Factorize 25x²- 100y²

solution

We use difference of two squares a² – b² = (a - b)(a + b)

25x²- 100y² = 5²x² - 10²y²

                     = (5x)² - (10y)²

                     = (5x - 10y)( 5x + 10y)

Hence 25x²- 100y² = (5x - 10y)( 5x + 10y)

TRY THIS…………….

Factorize 121x²- 4y²

LOGARITHMS 6

Evaluate Log30 – Log15 + Log50.

Solution

= Log30 – Log15 + Log50.

= Log(30 x 50)

               15

= Log(1500)

             15

= Log₁₀100

= Log₁₀10²

            

= 2Log₁₀10

= 2 x 1

= 2

∴ Log30 – Log15 + Log50 = 2

TRY THIS……………………….

Evaluate Log750 – Log15 + Log20.

GEOMETRY 2

A regular polygon has 12 sides. Find the total angles of that polygon.

Solution

n = 12

Total angles = (n - 2)180⁰

                   = (12 – 2)180⁰

                   = 10 x 180⁰

                   = 1800⁰

Total angles = 1800⁰

TRY THIS……………………….

A regular polygon has 17 sides. Find the total angles of that polygon.

RADICALS 3