Question

$3^{log_{x}3} = x^{9}$
3^(logx 3(основание х) = x^9

-x=x^9 получилось

Answer 1

ОДЗ: x>0 и х неравен 1
$3^{log_x 3}=3^{log_3 {x^9}} \\ log_x 3=log_3 {x^9} \\ \frac {1}{log_3 x}= 9 log_3 x \\ t=log_3 x \\ 1/t=9t \\ t^2=1/9 \\ t_1=1/3 <=> log_3 x=1/3 \\ x=3^{1/3} \\ t_2=-1/3 <=> log_3 x=-1/3 \\ x=3^{-1/3}$
Ответ: $3^{1/3}; 3^{-1/3}.$