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Консультация № 197029
10.11.2019, 04:24
0.00 руб.
1
1
1
Здравствуйте! Прошу помощи в следующем вопросе:
Решите уравнение.
Решите уравнение.
Прикрепленные файлы:
Обсуждение
19.08.2022, 09:34
общий
это ответ
Здравствуйте, svrvsvrv!
Требуется решить уравнение
Поскольку
является основанием логарифма, то по определению логарифма должны выполняться неравенства 
Для перехода к логарифмам по одному основанию воспользуемся тем, что
Тогда заданное уравнение можно переписать так:
В левой части последнего уравнения находится модуль (абсолютная величина) некоторого вещественного числа -- неотрицательное число. Поэтому и правая часть этого уравнения является неотрицательным числом, то есть
откуда следует, что 
Обозначим
(при этом 
). Тогда получим
Решим уравнение (1):
следовательно, у уравнения (1) нет вещественных корней.
Решим уравнение (2):
Следовательно, из двух корней уравнения (2) только второй удовлетворяет условию задачи, то есть
откуда 
Ответ:
Требуется решить уравнение
Поскольку
является основанием логарифма, то по определению логарифма должны выполняться неравенства Для перехода к логарифмам по одному основанию воспользуемся тем, чтоТогда заданное уравнение можно переписать так:
В левой части последнего уравнения находится модуль (абсолютная величина) некоторого вещественного числа -- неотрицательное число. Поэтому и правая часть этого уравнения является неотрицательным числом, то есть
откуда следует, что Обозначим
(при этом ). Тогда получимРешим уравнение (1):
следовательно, у уравнения (1) нет вещественных корней.
Решим уравнение (2):
Следовательно, из двух корней уравнения (2) только второй удовлетворяет условию задачи, то есть
откуда Ответ:
5
Большое спасибо!
Об авторе:
Facta loquuntur.
Facta loquuntur.
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