ОДЗ
{x>0
{x≠1
{log(x)√5x≥0
a)x∈(0;1)
√5x≤1⇒5x≤1⇒x≤0,2
0b)x∈(1;∞)
x≥0,2
x∈(0;0,2] U (1;∞)
log(x)√5x=log²(x)5
log²(x)5-1/2*(log(x)5+log(x)x)=0
log²(x)5-0,5log(x)5-0,5=0
log(x)5=a
a²-0,5a-0,5=0
a1+a2=0,5 U a1*a2=-0,5
a1=-0,5⇒log(x)5=-0,5⇒x^-0,5=5⇒x=1/25
a2=1⇒log(x)5=1⇒x=5