Question

Log5 (5-4x) = Log0.2 (X)

P.S. ответ - 0,25

Answer 1

ОДЗ: 0 < x < 1,25
$log_5(5-4x) = log_{5^{-1}}(x)\ log_5(5-4x) = -log_5(x)\ log_5(5-4x) + log_5(x) = 0\ log_5(5x-4x^2)=0\ 5x-4x^2=1\ 4x^2-5x+1=0\ D=25-16=9\ x_1= frac{5-3}{8} =0,25\ x_2= frac{5+3}{8} =1$

Ответ: 0,25 и 1