Solve` 3^((log_(9)x)^(2)-9/2log_(9)x+5)= 3 sqrt3.`

Explanation

We have`(log_(9)x)^(2) - 9/2 log_(9) x+ 5 = 3/2`
Putting ` log_(9)x = y," we have "y^(2)-9/2 y+5 = 3/2`
` or 2y^(2)-9y+7 = 0`,
` i.e.,(2y-7)(y-1) = 0`
` or y = 7//2, 1`
Therefore, either ` log_(9) x = 1 or log_(9) x = 7//2`
i.e., either ` x = 9 or x = 9^(7//2) = 3^(7)`