LOGARITHMS F6

 

BODMAS F1

 

Evaluate 90 + 50 x 3 – 80 ÷ 4

 

Solution

 

We apply BODMAS.

 

= 90 + 50 x 3 – 80 ÷ 4

 

= 90 + 50 x 3 – 20    [After dividing]

 

= 90 + 150 – 20    [After multiplying]

 

= 240 – 20    [After adding]

 

= 220       [After subtracting]

 

Hence 90 + 50 x 3 – 80 ÷ 4 = 220      

 

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

 

Evaluate 200 + 10 x 30 – 60 ÷ 4

LOGARITHMS F5

 Evaluate Log60 – Log0.42 + Log700.

 

Solution

 

= Log60 – Log0.42 + Log700.

 

= Log(60 x 700)

               0.42

 

= Log(42000)

             0.42

 

= Log(4200000)

              42

 

 

= Log 100,000

             

 

= Log₁₀100,000

 

= Log₁₀10⁵

            

= 5Log₁₀10

 

= 5 x 1

 

= 5

 

∴ Log60 – Log0.03 + Log50 = 4

 

TRY THIS……………………….

 

Evaluate Log60 – Log1.2 + Log2000

BANKING F1

 

Asad deposited the amount of 200,000/= in a bank for 3 years and got a profit of 66000/=. Find the interest rate?

 

Solution

 

I = 66000/=, P = 200,000/=, T = 3 years, R = ?

 

I  = PRT

      100

 

66,000  = 200000 x R x 3

                      100

 

66,000  = 200000 x R x 3

                      100

 

66,000  = 2000 x R x 3

                     

66,000  = 6000R

          

¹¹66,000  = 6000R

   6000       6000

 

Hence the interest rate was 11%

 

TRY THIS…………………..

 

Sonali deposited the amount of 70,000/= in a bank for 5 years and got a profit of 10,500/=. Find the interest rate?

 

 

LOGARITHMS F4

 

EXPONENTIALS F2

 If y⁵ = 6, find y¹⁵.

 

Solution

 

= y¹⁵

 

= (y⁵)³

 

= (6)³      remember y⁵ = 6

 

= 6 x 6 x 6

 

= 216

 

Hence y¹⁰ = 121.

 

TRY THIS……………….

 

If  y¹⁵ = 4, find y⁶⁰.

LOGARITHMS F3

 If Log_ax = 4, find Log_a(¹/x⁴⁴)

Solution

= Log_a(¹/x⁴⁴)

= Log_ax^-44          [since 1/aⁿ = a^-n]

= -44 x Log_ax    [since Log_axⁿ   = nLog_ax ]

= -44 x 4

= -176 answer

TRY THIS………..

If Log_ab= 12, find Log_a(¹/b²⁰)

SIMPLIFY F1

 

Simplify the expression w² - t²/ (w + t)

 

Solution

 

From difference of two squares p² - q² = (p - q)(p + q)

 

= w² - t²/ (w + t)

 

= (w + t)(w - t)

      w + t

 

= (w + t)(w - t)

      w + t

 

=  w - t    answer

      

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

 

 

Simplify the expression 

 

u² - w²/ (u + w)

FUNCTIONS F1

 

FACTORIZE F1

 Factorize completely 2t – 98t³

 

Solution

 

= 2t – 98t³ 

 

= 2t(1 – 49t²)

 

= 2t(1 – 7²t²)

 

= 2t[(1)² – (7t)²]

 

From difference of two squares, a² – b² = (a-b)(a+b)

 

= 2t[(1 – 7t)(1 + 7t)]

 

= 2t(1 – 7t)(1 + 7t) answer

 

TRY THIS……………..

 

Factorize completely 3m – 48m³