Предмет: Алгебра, автор: 0755tipzsb

Решите уравнение: log9 (2x-3)+log9 (2x-5) + log9 (2x-5) = 1/2(это одна вторая).​

Ответы

Автор ответа: MrSolution
0

Ответ:

(см. объяснение)

Объяснение:

\log_9(2x-3)+\log_9(2x-5)+\log_9(2x-5)=\dfrac{1}{2}

Поскольку каждое слагаемое левой части уравнения есть возрастающая функция, то вся левая часть уравнения представляет из себя возрастающую функцию.

Тогда существует не более одного такого x, при котором равенство верно.

Заметим, что x=3 корень уравнения.

Выше показано, что других корней нет, а значит уравнение решено.

Задание выполнено!

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