Log√2x>4

log4 (3x-2) <3

log√6 (x-4) + log√6 (x+1) ≤2

1

log (√2) x>4

x> (√2) ^4

x>4

x∈ (4; ∞)

2

{3x-2>0⇒3x>2⇒x>2/3

{3x-2<64⇒3x<66⇒x<22

x∈ (2/3; 22)

3

{x-4>0⇒x>4

{x+1>0⇒x>-1

{log (√6) [ (x-4) (x+1) ]≤2⇒x²-3x-4≤6

x²-3x-10≤0

x1+x2=3 U x1*x2=-10⇒x1=-2 U x2=5

-2≤x≤5 U x>4⇒x∈ (4; 5]