Question

Решите неравенство................................................................

Answer 1

3^x=a
a³-9a²-(9a²-486)/(a-6)-81≤0
(a^4-6a³+54a²+9a²-486-81a+486)/(a-6)≤0
(a^4-15a3+63a²-81a)/(a-6)≤0
a(a³-15a²-81)/(a-6)≤0
a[a²(a-3)-12a(a-3)+27(a-3)]/(a-6)≤0
a(a-3)(a²-12a+27)/(a-6)≤0
a(a-3)[a(a-3)-9(a-3)]/(a-6)≤0
a(a-3)²(a-9)/(a-6)≤0
a=0  a=3  a=9  a=6
           _                +                +                _                +
---------------[0]------------[3]--------------(6)----------[9]-----------------
a≤0⇒3^x≤0 нет решения
a=3⇒3^x=3⇒x=1
6<a≤9⇒6<3^x≤9⇒log(3)6<x≤2
x∈(log(3)6;2] U {1}