(log₃x)²-I(log₃x)I<2<br>заменим I(log₃x)I =t ≥0
т.к. (log₃x)² = I(log₃x)I² , тогда (log₃x)²-I(log₃x)I<2 t²-t <2 <span>t²-t-2 <0 </span>
t ≥0 ⇔ t ≥0
t²-t-2 = 0 t1=-1 t2=2
+ - - +
-------------(-1)--//-----------0-------///-------2------------
i-----///------------------------------------
0≤t≤2 ⇔ I(log₃x)I≤2 ⇔ -2≤(log₃x)≤2 ⇔3∧(-2)≤x≤3∧2 ⇔ 1/9≤x≤9
ответ: 1/9≤x≤9