Question

Распишите подробно решение:

$X^{ log _{3}X-2 } = 27$

Answer 1

$X^{ log _{3}(x-2) } = 27 \ \ log_x(27)=log_3(x-2) \ \ frac{1}{log_{27}(x)} =log_3(x-2) \ \ frac{1}{log_{3^3}(x)} =log_3(x-2) \ \ frac{1}{ frac{1}{3} log_{3}(x)} =log_3(x-2) \ \ frac{3}{log_3(x)} =log_3(x-2)$


$frac{3}{x} =x-2 \ \ 3=x(x-2) \ x^2-2x-3=0 \ D=4-4*(-3)=4+12=16 \ x_1=3 \ x_2=-1$