Paper 4: Fundamentals of Business Mathematics & Statistic

2.38 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Algebra

or, (0.1234) 10 10a× a= c

or, (0.1234) 10a= c a−

or,

c a

(0.1234) 10a

−

= ....... (i)

and(1.234) 10 0.1234 10b= c cb ....... (ii)

From (I) and (II), we get

caa bc c a c

(^1010) a b bc ab ac

− −

= ⇒ = ⇒ − =

1 1 1

⇒a c b− =

Example 57: Find the simplest value of

{ ( ) }

1 13

3 1

1 1 1 1 x

− −

−

− − −

when x = 0, x = 0.1

Solution :

1 31

3

1 1 1^1

1 x

− −

   

=− − −  

   

1 31

3

3

1 11 x 1

1 x

− −

  − − 

=−  

  −  

1 31

3

3

1 1 x

1 x

− −

 −  

=−  

  −  

3 31

3

1 11 x

x

−

=^ −^ −^

(^) −
3 31 3 3 31
3 3
1 1 x x 1 x
x x
− −
=+ −  = + − 
   
   
31 1
(^13) x (^33) x 0 when x 0
x
−
=  =  = = =
    
=0.1when x 0.1=