5^[log(5)(x+4)*log(5)[(x³-9x)/(x+4)]]=5^log(5)[(x+4)(x³-9x)/(x+4)]=
=5^log(5)(x³-9x)=x³-9x,x≠-4
ОДЗ
{x+4>0
{x(x-3)(x+3)/(x+4)>0
+ _ + _ +
---------(-4)-----------(-3)----------(0)------------(3)-----------------
x<-4 U -3<x<0 U x>3
x∈(-3;0) U (3;∞)
(x³-9x)`=3x²-9=3(x-√3)(x+√3)=0
+ _ +
---------------(-√3)--------------(√3)----------
max
(-√3)³-9*(-√3)=-3√3+9√3=6√3 значение функции в точке максимума