4,5,6 Пожалуйста подробно решите, хотя бы один номер из трёх

5^x - 3^(x+1) >=2*(5^(x-1) - 3^(x-2) )
5^x - 3*3^x >=2*( 1/5 *5^x - 1/9*3^x)
1-3*y >=2*(1/5-1/9*y),
y = (3/5)^x;
1-2/5 >= (3-2/9)*y
3/5 >=25/9*y
y<=27/125 = (3/5)^3
(3/5)^x <=(3/5)^3
(3/5)^(x-3) <=1
x >=3


4.
2^(log(x))^2 +x^log(x) = 32
log(x) = y -> x = 2^y

2^(y^2) + (2^y)^y = 2^5
2*2^(y^2) = 2^5 -> y^2 = 4 -> y = +-2
x1 = 4
x2 = 1/4
log(x1) = 2 -> log(x1)^2 = 4
log(x2) = -2; -> log(x2)^2 = 4