Question

Loga(b) =3/2, logc(d) =5/4 if a-c=9 then value of (b-d) is

Answer 1

b = a3/2 ; d= c5/4

let a1/2 = x and c1/4 =y

then b = x3 and d = y5

given a-c = 9 or x2 - y4 = 9 or (x-y2)(x+y2)=9

we have to find two factors of 9 which are integers

now ; 9 can be expressed as 9x1 or 3x3

i.e. if we breah 9 as 3x3 then x-y2 = x+y2 which is not possible for any existing integer

therefore x-y2 = 1 and x+y2 = 9

adiing the two equations we get 2x = 10 or x=5

and if x = 5 then y = 1

therefore b = 125 and d =32

therefore b-d = 83