Question

Помогите, пожалуйста с решением неравенства -2logx/3 27>=log3 27x+1

Answer 1

-2*3log(x/3) 3≥log(3) 27+log(3) x +1
-6*log(3) 3/log(3) x-log(3) 3≥3+log(3) x +1
log (3) x=t
-6/t-1≥t+4
t+4+6/(t-1)≤0
(t+4)(t-1)+6/t-1≤0
t²+4t-t-4+6/t--1≤0
t²+3t+2/t-1≤0
(t+1)(t+2)/t-1≤0
t≤-2  и  -1≤t<1

log(3) x ≤-2
$\left \{ {{x>0} \atop {x \leq 3^{-2} }} \right.$
$\left \{ {{x>0} \atop {x \leq \frac{1}{9} }} \right.$
0<x≤1/9

-1≤log(3) x <1
1/3≤x<3
ответ x∈(0;1/9]v{1/3;3)