Question

Решите уравнение 2logx √3 - 1 = log₈₁ x⁸

Answer 1

x>0 U x≠1
log(x)3 -1 =2/log(x)3
log²(x)3-log(x)3-2=0
log(x)3=a
a²-a-2=0
a1+a2=1 U a1*a2=-2
a1=-1⇒log(x)3=-1⇒1/x=3⇒x=1/3
a2=2⇒log(x)3=2⇒x²=3⇒x=√3 U x=-√3-не удов усл
Ответ х=1/3,х=√3