Question

помогите решить логарифмическое уравнение

Answer 1

ОДЗ : x > 0

$log_{3}^{2} x-log_{3}x-2=0\\\\log_{3}x=m\\\\m^{2}-m-2=0\\\\D=(-1)^{2}-4*(-2)=1+8=9=3^{2}\\\\m_{1}=\frac{1+3}{2}=2\\\\m_{2} =\frac{1-3}{2}=-1\\\\log_{3}x=2\\\\x_{1}=9\\\\logx_{3}x=-1\\\\x_{2}=\frac{1}{3} }$