Solve ` 2 log_(3) x - 4 log_(x) 27 le 5`.

Explanation

Let ` log_(3) x = y`
` rArr x = 3^(y)` (i)
Therefore, the given inequality becomes ` 2log_(x) x - 12 log_(x) 3 le 5`
` or 2y - 12/y le 5`
` or 2y^(2) - 5y - 12 le 0`
` or (2y+3)(y-4) le 0`
` rArr y in [-3/2 , 4]`
` rArr - 3/2 le log_(3) x le 4`
` rArr 3^(-3//2) le x le 81`