If `3^(x+y)=81` and `81^(x-y)=3`, then the value of `x/y` is

Options

A. `15/17`
B. `17/30`
C. `15/34`
D. `17/15`

Answer

D

Explanation

According to the question
`implies3^(x+y)=81` and `81^(x-y)=3`
`implies3^(x+y)=(3)^(4)` and `(3)^(4(x-y))=3`
`impliesx+y=4` and `x-y=1/4`
`x+y=4`…………i
`x-y=1/4`……….ii
Solve equation i and ii
`x=17/8, y=15/8, x/y=17/15`