LOGARITHMS K8

 Log₃27 + Logx =8. Find x

 

Solution

 

Log₃27 + Logx =8

 

Log₃3³ + Logx =8

 

3Log₃3 + Logx =8

 

(3 x 1) + Logx =8

 

3 + Logx =8

 

Logx =8 - 3

 

Logx =5

 

Log₁₀x =5 [Since any log without a base it is a base 10 logarithm]

 

x = 10⁵  [after changing logarithmic form into exponential form]

 

x = 100,000 answer. 

TRY THIS………….

 

Log₅625 + Logu =9. Find u

SETS K3

 There are 37 villagers at the meeting. 12 are farmers and 18 are workers and 8 are both farmers and workers. How many villagers are

i)                 Either farmers or workers.

ii)             Neither farmers nor workers

 

Solution

 

n(U)=37

n(F)=12

n(W)=18

n(FnW)=8

n(FuW)=?

n(FuW)’=?

 

i)  n(FuW) = n(F) + n(W) - n(FnW)

n(FuW) = 12 + 18 - 8

n(FuW) = 30 – 8

n(FuW) = 22

 

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n(U) = n(FuW) + n(FuW)’

37 = 22+ n(FuW)’

37 - 22=n(FuW)’

15=n(FuW)’

 

Hence those who are neither farmers nor workers are 15

 TRY THIS.....................

 There are 40 villagers at the meeting. 12 are farmers and 18 are workers and 6 are both farmers and workers. How many villagers are

i)                 either farmers or workers.

ii)             neither farmers nor workers

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ALGEBRA K9

 

Expand y(y – 4)(y – 10)

 

Solution

 

= y(y – 4) (y – 10)

 

= y[y (y – 10) – 4 (y – 10)]

 

= y[y² – 10y – 4y + 40] 

 

= y³ – 14y² + 44y

 

= y³ – 14y² + 44y    answer

 

TRY THIS………..

 

Expand w(w – 9) (w – 10)

PROFIT AND LOSS K4

 

Jemson bought a radio at 50,000/= and after one year he sold it at a loss of 14%. Find the price of a radio after a year.

 

Solution

 

= 50,000 - (14% of 50,000)

= 50,000 - (0.14 of 50,000)  after dividing 14% by 100

= 50,000 - 7,000

= 43000/= 

 

Hence the new price is 43000/=    

 

TRY THIS………….

 

Patson bought a radio at 70,000/= and after one year he sold it at a loss of 24%. Find the price of a radio after a year.

LOGARITHMS K6

 

If Log_ax = 0.82, find Log_a(¹/x⁷)

 

Solution

 

= Log_a(¹/x⁷)

 

= Log_ax^-7

 

= -7 x Log_ax

 

= -7 x 0.82

 

= -5.74

 

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If Log_ac= 60, find Log_a(¹/c⁵)

ALGEBRA K8

 

Expand (y – 4)(y – 10)

 

Solution

 

= (y – 4) (y – 10)

 

= y (y – 10) – 4 (y – 10)

 

= y² – 10y – 4y + 40     [Since -4 x -40 = +40]

 

= y² – 14y + 44 answer

 

TRY THIS………..

 

Expand (w – 9) (w – 10)