Log6 (5x-2) >3 log6 2+2

Log₆ (5x-2) >3log₆2+2

log₆ (5x-2) >log₆2³+2

log₆ (5x-2) - log₆8>2

log₆ ((5x-2) / 8) >2

2=log₆6²=log₆36

log₆ ((5x-2) / 8) >log₆36

6>1, знак не меняем

{5x-2>0 {5x>2 {x>2,5

(5x-2) / 8>36 5x-2>288 x>57,2

x>57,2.

x∈ (57,2; ∞)