2^x=a
a³-9a²+(9a²-288)/(a-9)-32≤0
(a^4-9a³-3a³+27a²+9a²-288-32a+288)/(a-9)≤0
(a^4-12a³+36a²-32a)/(a-9)≤0
a(a³-12a²+36a-32)/9a-9)≤9
a[a²(a-2)-10a(a-2)+16(a-2)]/(a-9)≤0
a(a-2)(a²-10a+16)/(a-9)≤0
a(a-2)[a(a-2)-8(a-2)]/(a-9)≤0
a(a-2)²(a-8)/(a-9)≤0
a=0 a=2 a=8 a=9
_ + + _ +
------------[0]-------------[2]-------------[8]------------(9)-------------------
a≤0⇒2^x≤0 нет решения
a=2⇒2^x=2⇒x=1
8≤a<9⇒8≤2^x<9⇒3≤x<log(2)9<br>Ответ x∈[3;log(2)9) U {1}