Предмет: Алгебра, автор: Afaxriya2001

Помогите с логарифмом.....

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Ответы

Автор ответа: artalex74

x>0, x≠1
Обе части логарифмируем по основанию 5:
$\log_5x^{\log_5x-2}=\log_5125\\ (\log_5x-2)*\log_5x=3\\ log_5x=t\\ (t-2)t=3\\ t^2-2t-3=0\\ t_1=-1,\ t_2=3$
Отсюда
$1)\ log_5x=-1\ \Rightarrow x= \frac{1}{5}=0,2 \\ 2)\ log_5x=3\ \Rightarrow x= 5^3=125 \\$
Ответ: 0,2; 125,

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