Log(9x) 27 <= 1/log(3) x

Question

Log(9x) 27 <= 1/log(3) x<br>

Answer 1

X>0
3/(log(3)x+2)-1/log(3)x≤0
(3log(3)x-log(3)x-2)/log(30x(log(3)x+2)≤0
2(log(30x-1)/log(3)x(log(30x+2)≤0
log(30x=a
2(a-1)/a(a+2)≤0
a=1  a=0  a=-2
           _                  +                     _                    +
----------------(-2)----------(0)---------------[1]-------------------
a<-2⇒log(30x<-2⇒x<1/9<br>0x∈(0;1/9) U (1;3]