Question

Let `a , b , c , d` be positive integers such that `(log)_a b=3/2a n d(log)_c d=5/4dot` If `(a-c)=9,` then find the value of `(b-d)dot`

Answer 1

`b=a^(3/2),a=b^(2/3)`
`d=c^(5/4),c=d^(4/5)`
`a-c=9`
`b^(2/3)-d^(4/5)=9`
`b^(2/3)=9+d^(4/5)`
`b=(9+d^(4/5))^(3/2)`
`b=125,d=32`
`a=b^(2/3)=25`
`c=(32)^(4/5)=16`
`a-c=25-16=9`
`b-d=125-32=93`.