Log 3 Log 1/2 log 1/3 x>0

Question

Log 3 Log 1/2 log 1/3 x>0

Answer 1

Log3 log 1/2 log 1/3 x > log 3 1
log 1/2 log 1/3 x >1
log 1/2 log 1/3 x > log 1/2 1/2
log 1/3 x < 1/2
log 1/3 x < log 1/3 (1/3)^(1/2)
x > (1/3)^(1/2)
x> √3/3