(1/2)ˣ⁺²+3*(1/2)ˣ⁺¹-(1/2)ˣ<3<br>(1/2)²*(1/2)ˣ +3*(1/2)*(1/2)ˣ -(1/2)ˣ<3<br>(1/2)ˣ* ((1/4) +(3/2) - 1)<3<br>(1/2)ˣ *(3/4)<3<br>(1/2)ˣ< 3 : (3/4) т.к.( 1/2 )<1 , меняем знак на противоположный<br>(1/2)ˣ< 4
(1/2)ˣ< (1/2)⁻²
х>-2
x∈(-2; +∞)
(㏒₃х)²+2㏒₃х-3≤0 замена ㏒₃х=а ОДЗ х>0
а²+2а-3=0
D=4+12=16 √D=4
a=(-2+4)/2=1 ㏒₃х=1 x=3
a=(-2-4)2=-3 не подходит под ОДЗ