Solve : `log_(x^(2)16+log_(2x)64=3`.

Answer

`x=2^(-1//3),4`

Explanation

`log_(x^(2))16+log_(2x)64=3`
`rArr (4)/(log_(2)x^(2))+(6)/(log_(2)x)=3`
Put `log_(2)x=t`
`rArr (2)/(t)+(6)/(1+t)=3`
`rArr 2+2t+6t=3t+3t^(2)`
`rArr 3t^(2)-5t-2=0`
`rArr (3t+1)(t-2)=0`
`rArr t=-(1)/(3), t=2`
`rArr log_(2)x=-(1)/(3)` or `log_(2)x=2`
`rArr x=2^(-1//3)` or x = 4