LOGARITHMS 1

 Simplify Log₂128 – Log₅3125 – Log₆7776

 

Solution

 

= Log₂128 – Log₅3125 – Log₆7776

 

= Log₂2⁷ – Log₅5⁵ – Log₆6⁵

 

= 7Log₂2 – 5Log₅5 – 5Log₆6  because Log_aaⁿ =  nLog_aa

 

= (7 x 1) – (5 x 1) – (5 x 1)    

 

= 7 – 5 - 5

= 7 – 0

 

= 7

 

Hence Log₂128 – Log₅3125 – Log₆7776 = 7 

 

TRY THIS…………..

 

Simplify Log₂2048 – Log₃243 – Log₅3125

SIMPLIFY

 Simplify 44

               8^-4/3

 

Solution

 

=  44

    8^-4/3

 

= 44 x 1

           8^-4/3

 

=  44 x 8^4/3        [Since 1/a^-n = aⁿ]

 

=  44 x (8^1/3)⁴        [Since 8^1/3 = cube root of 8 = 2]

 

=  44 x (2)⁴        

 

=  44 x 16

 

= 704     

          

Hence   44        = 704

              8^-4/3

 

TRY THIS…..

simplify 24

              64^-2/3

 

X-INTERCEPT

 If 3x + 7y - 56 = 0; find x-intercept.

Solution

x-intercept is when y=0.

3x + 5y -56 = 0

3x + 5(0) - 56 = 0

3x - 56 = 0

3x = 0+ 56

3x = 56

3      3

 

x= 56/3

Hence x-intercept= 56/3 

TRY THIS………..

If 11x - 7y - 30 = 0; find x-intercept.

LOGARITHMS

If log 2= 0.3010; find the value of log 12500 without using tables.

Solution

=log12500

=log(100,000 ÷8)

=log100,000 –log8

= log10⁵ - log2³

= 5log10 - 3log2

=(5 x 1) - (3 x 0.3010)

= 5  -  0.9030

=4.097

Hence log 1250 =4.097  

TRY THIS……………

If log 2= 0.3010; find the value of log 25,000 without using tables.

MID POINT 1

Find a and b if the midpoint of a line from (a, 6) to (8, b) is

(30, 7)

Solution

x1=a, x2=8, y1=6, y2=b.

(30, 7)= (x1 + x2, y1 + y2)

                   2             2

(30, 7)= (a + 8,  6 + b)

                  2          2

Equating equal values of x;

30= a + 8

         2      

2 x 30= (a + 8)  x 2 ¹

                2 ₁     

60 = a + 8

60-8 = a

a = 52.

Equating equal values of y;

7 = 6 + b

        2

2 x 7= (6 + b)  x 2 ¹  multiplying by 2 both sides.

                2 ₁     

14 = 6 + b

14 – 6 = b

b = 8

Hence a = 52 and b=8

TRY THIS……………………..

Find m and n if the midpoint of a line from (m, 19) to (13, n) is (9, 11)

POLYGONS 1

Find the exterior angle of a regular polygon with 18 sides.

Solution

n = 6

e =   360

         n

e =   360

        18

e =   360 ²⁰

        18₁

e = 20⁰

Hence the exterior angle is 20⁰

TRY THIS………………………………………..

Find the exterior angle of a regular polygon with 12 sides.

PRIME FACTORS 1

Write 560 as a product of prime factors.

Solution

2	560
2	280
2	140
2	70
5	35
7	7
	1

 Then, 480 = 2 x 2 x 2 x 2 x 5 X 7

Hence   480 = 2⁴ x 5 x 7.

TRY THIS........

Write 1000 as a product of prime factors.

SETS 1

If n(B)= 60 , n(AuB) = 170 and n(AnB)=10, find n(A)

Solution

n(AuB) = n(A) + n(B) - n(AnB)

  170    = n(A)  + 60– 10

  170     = 60 -10 + n(A) 

  170     = 50 + n(A) 

  170 - 50        = n(A)

  120        = n(A)

Hence n(A) = 120 answer

TRY THIS…………………………….

If n(B)= 55 , n(AuB) = 169 and n(AnB)=16, find n(A)

ANGLES 1

If A and B are supplementary angles such that A = 27° and B = x + 55° , find the value of x .

Solution

A + B = 180⁰. [Since supplementary angles add up to 180⁰]

27⁰ + x + 55⁰ = 180⁰.

x + 82⁰ = 180⁰.

x = 180⁰ - 82⁰

x = 98⁰  answer.

TRY THIS.............................. 

If A and B are supplementary angles such that A = 53° and B = x + 42° , find the value of x .

EXPONENTIALS 1

If a² = 3; find the value of a¹⁰ + a⁸.

solution

=a¹⁰ + a⁸.

=(a²)⁵ + (a²)⁴.

=(3)⁵  +  (3)⁴

=243 + 81

=324 answer  

  

TRY THIS.........................

If a² = 5; find the value of a¹⁰ - a⁶.