Question

Find the value of x satisfying the equations `log_(3)(log_(2)x)+log_(1//3)(log_(1//2)y)=1` and `xy^(2)=9`

Answer 1

Correct Answer - x=729
`log_(3)(log_(2)x)+log_(1//3)(log_(1//2)y)=1`
`rArr log_(3)(log_(2)x)-log_(3)(-log_(2)y)=1`
`rArr log_(3)(-(log_(2)x)/(log_(2)y))=1`
`rArr -(log_(2)x)/(log_(2)y)=3`
`rArr xy^(3)=1`
Also, `xy^(2)=9`
`rArr =(1)/(9)`
`therefore x=729`