Question

x^(log(3) x - 2) = 27 Найдите x​

Answer 1

$x^{log_{3}x-2 }=27\\\\log_{3}x^{log_{3}x-2 }=log_{3} 27\\\\(log_{3}x-2)log_{3}x=3\\\\log_{3}^{2}x-2log_{3}x-3=0\\\\\left[\begin{array}{ccc}log_{3}x=3 \\log_{3}x=-1 \end{array}\right\\\\\\\left[\begin{array}{ccc}x=27\\x=\frac{1}{3} \end{array}\right\\\\Otvet:\boxed{27 \ ; \ \frac{1}{3}}$