Question

x^(log(3) x - 2) = 27 Найти значение х

Answer 1

x^(log3 (x) - 2) = 27

Прологарифмируем по основанию 3 
log3 x^(log3(x) - 2 ) = log3 (27)
log3(x) * (log3(x) - 2) = 3
log ² 3(x) - 2log3(x) - 3 = 0 
log3(x) = t

t^2 - 2t - 3 = 0 
D = 4 + 12 = 16 = 4^2
t1 = ( 2 + 4)/2 = 6 /2 = 3
t2  =( 2 -  4)/2 = - 2/2 = - 1

log3(x) = 3
x = 3^3
x = 27

log3(x) = - 1
x = 3^(-1)
x = 1/3

Ответ
1/3; 27