Ответы
Ответ дал:
0
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](https://tex.z-dn.net/?f=log_5%285-4x%29+%3D+log_%7B5%5E%7B-1%7D%7D%28x%29%5C%0Alog_5%285-4x%29+%3D+-log_5%28x%29%5C%0Alog_5%285-4x%29+%2B+log_5%28x%29+%3D+0%5C%0Alog_5%285x-4x%5E2%29%3D0%5C%0A5x-4x%5E2%3D1%5C%0A4x%5E2-5x%2B1%3D0%5C%0AD%3D25-16%3D9%5C%0Ax_1%3D+frac%7B5-3%7D%7B8%7D+%3D0%2C25%5C%0Ax_2%3D+frac%7B5%2B3%7D%7B8%7D+%3D1 "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
Ответ: 0,25 и 1
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