LOGARITHMS F6

 Simplify Log₂1024 - Log₃81

 

Solution

 

= Log₂1024 - Log₃81

 

= Log₂2¹⁰ - Log₃3⁴    [Since 1024=2¹⁰ and 81=3⁴].

 

= 10Log₂2 - 4Log₃3    [since Log_CC = 1]

 

= (10 x 1) - (4 x 1)

 

= 10 - 4

 

= 6

 

Hence Log₂1024 - Log₃81 = 6

 

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

 

Simplify Log₂2048 – Log₅125 

RADICALS F1

 

FUNCTIONS F2

 

If F(x) = 2x + 60; Find F^-1(x).

 

Solution

 

HINT: F^-1(x) means inverse.

 

PROCEDURE:

Make x the subject and then interchange x and y variables.

 

Let y=F(x)

 

So,  y= 2x + 60

 

y – 60 = 2x

 

y – 60  = 2x

   2          2

 

y – 60   = x

   2

 

x  =   y – 60     after rearranging

           2

 

 y^-1 = x – 60     after interchanging x and y variables.

             2

 

F^-1(x) = x – 60     after interchanging x and y variables.

                2

 

Hence, F^-1(x) = x – 60     

                             2

 

TRY THIS……………………………

 

If F(x) = 4x - 26; Find F^-1(x).

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)