LOGARITHMS 2

If Log(30x-90/5+x) = 1. Find x.

Solution

Log(30x-90/5+x) = 1.

Log₁₀(30x-90/5+x) = 1.

 30x-90 = 10¹. After changing into exponential form

   5+x

30x-90 = 10    since [10¹=10]

   5+x

30x-90 = 10(5+x)    after cross multiply

  

30x-90 = 50+10x

30x-10x = 50+90 [collecting like terms]

20x = 140

x=7  [after dividing by 20 both sides]

Hence x=7.

TRY THIS……………

If Log(30x-50/5+x) = 1. Find x.

SETS 1

If n(A)= 85 , n(B)= 96 and n(AuB)= 140, find n(AnB).

Solution

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

140 = 85 + 96 - n(AnB)

140 = 181 - n(AnB)

140 - 181 = - n(AnB)

-41 = -n(AnB)

n(AnB) = 41 [after dividing by -1 both sides]

Hence n(AnB) = 41 answer

TRY THIS………….

If n(A)= 90 , n(B)= 96 and n(AuB)= 139, find n(AnB).

LOGARITHMS 1

  Evaluate Log60 – Log0.3 + Log500.

Solution

= Log60 – Log0.03 + Log500.

= Log(60 x 500)

               0.03

= Log(30000)

             0.03

= Log(3000000)

              3

= Log 1,000,000

             

= Log₁₀1,000,000

= Log₁₀10⁶

            

= 6Log₁₀10

= 6 x 1

= 6

∴ Log600 – Log0.03 + Log50 = 6

TRY THIS……………………….

Evaluate Log6,000 – Log4.8 + Log80,0000

SIMPLIFY 1

Simplify 21x-3(x-y)+5

Solution

=21x-3(x-y)+5

=21x-3x+3y+5

=18x+3y+5 answer

TRY THIS……..

Simplify 44x-9(x-y)+17

ACCOUNTS 1

Prepare a profit and loss account for the year ended 31^ST May, 2015 from the following balances:

Transport     sh. 69,000

Advertising Sh. 60,000

General expenses sh 35,000

Sundry expenses sh 4,000

Interest received sh. 32,000

Carriage sh 42,000

Gross profit  sh 122,000

Solution

Dr      PROFIT AND LOSS ACCOUNT FOR THE YEAR ENDED ON 31TH, MAY-2011               Cr
Particulars	Folio	Amount	Particulars	Folio	Amount
Transport		69,000	Gross profit	b/d	122,000
Advertising		60,000	Interest received		32,000
General expenses		35,000	Net Loss		56,000
Sundry expenses		4,000
Carriage		42,000
		210,000			210,000

TRY THIS………..

Prepare a profit and loss account for the year ended 31^ST September, 2016 from the following balances:

Transport -----------------------sh. 76,000

Advertising ---------------------Sh. 58,000

General expenses------------- sh 37,000

Sundry expenses ----------------sh 9,000

Interest received------------- sh. 32,000

Carriage -------------------------sh 23,000

Gross profit--------------------sh 116,000

EARTH AS SPHERE 1

Change 700 nautical miles into kilometers.

Solution

1 nautical mile= 1.852 km

700 nautical mile= ?

 = 1.852 x 700

          1

=1296.4

=1296.4 to 1 d.p

Hence 700 nautical miles= 1296km.

TRY THIS…………….

Change 60 nautical miles into kilometers

PROBABILITY 1

A bag contains 4 red balls and 6 blue balls. Two balls are taken from the bag. What is the probability that they are both red?

Solution

(This is a problem with replacement)

n(R) = 4, n(B) = 6, n(S) = 10

P(R) = n(R)

            n(S)

P(R) = 4

          10

1st pick = ⁴/10

2nd pick = ⁴/10 as well.

P(RR) =  4      x    4

             10           10

P(RR) =   ¹⁶ /100 = ⁴/25       

Therefore Probability of drawing a red ball is 4/25     

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

A bag contains 9 purple stones and 11 blue stones. Two stones are taken from the bag. What is the probability that they are both purple?

SEQUENCE&SERIES 1

The 1st term of arithmetic progression is 63 and the common difference is 40. Find the nth term

solution

A1=63, d= 40, n=?

An =A1 + (n-1) d

An=63 + (n-1)40 

An=63 + 40n -40

An=40n + 63-40

An=40n + 23

Hence the nth term is An=40n + 23  

TRY THIS………………….. 

The 1st term of arithmetic progression is 144 and the common difference is 77. Find the nth term

LOGARITHMS 5

Evaluate Log1,000,000,000 +  log 0.01 + log₃243

Solution

= Log1,000,000,000 +  log 0.01 + log₃243

= Log10⁹ +  log 10^-2 + log₃3^-5

= 9Log10 +  (-2log 10) + (-5log₃3)

= (9x1) + (-2x1) + (-5x1)

= 9 + (-2) + (-5)

= 2

Hence Log1,000,000,000 +  log 0.01 + log₃243 = 2

TRY THIS……………..

Evaluate Log100,000,000 +  log 0.0001 + log₃81

EXPONENTIALS 3

Simplify (6a)² - 3a². 

 

Solution

= (6a)² - 11a²    

= 6².a² - 11a²               Since (mn)² =m² . n²

= 36a² - 11a²   {since the square number of 6 is 36}

= 25a²

TRY THIS………………

Simplify (8m)² – 45m².