Question

Log(b)/log(a)=3/2 and log(d)/log(c)=5/4 and a-c=9 then b-d=?

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 breadth 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