Question

(log5x)^2-2=3log125x
Помогите решить плз.

Answer 1

(log5x)^2 - 2 - 3log125x = 0 
(log5x)^2 - 2 - 3log5^3(x) = 0 
(log5x)^2 - 2 - 3/3*log5(x) = 0 
(log5x)^2 - log5(x) - 2= 0 

Пусть log5(x) = t, тогда 
t^2  - t - 2 = 0 
D = 1 + 8 = 9 
t1 = ( 1 + 3)/2 = 2
t2 = (1 - 3)/2 = - 1

Обратная замена
log5(x) = 2
x = 5^(2)
x = 25

log5(x) = - 1
x = 5^(-1)
x = 0,2

Ответ
0,2; 25