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Решить уравнение. Логарифм по основанию 11 от (11+х)^5=(Логарифм по основанию 2 от (16-х))*Логарифм по основанию 11 от (11+х)
Обсуждение
Неизвестный
04.06.2009, 13:12
общий
06.06.2009, 01:31
это ответ
Здравствуйте, Nightwalker.
log_11(11+x)^5=log_2(16-x)*log_11(11+x);
ОДЗ: 11+x>0; 16-x>0 => x>-11; x<16 => x в (-11,16)
Решаем: log_11(11+x)^5=log_2(16-x)*log_11(11+x); 5*log_11(11+x)=log_2(16-x)*log_11(11+x); x не равно -10; 5=log_2(16-x); 2^5 = 16-x; 32=16-x; x=-16 - не входит в ОДЗ
Ответ: уравнение решений не имеет
5
Неизвестный
04.06.2009, 13:14
общий
Спасибо. вот и у меня так получилось..а это Б4 на ЕГЭ..туда нельзя написать "нет решений"
хотя задание стоит "если несколько корней, то написать их сумму". Логично думаю написать будет 0, если корни отсутствуют
Неизвестный
04.06.2009, 13:18
общий
Может там должно быть (16+х), тогда было бы нормально, в итоге уравнение 16+x=32, x=16 попадало бы в ОДЗ
Неизвестный
04.06.2009, 13:29
общий
ну пишите все равно что нет решения или значок пустого множества (перечеркнутый ноль), это будет означать, что множество решений уравнения является пустым, что то же что и "нет решения"
Неизвестный
04.06.2009, 13:34
общий
x=-10 разве не является решением?
Неизвестный
04.06.2009, 13:36
общий
это ответ
Здравствуйте, Nightwalker!
Ответ существует, пустое мн-во - это неверный ответ. Когда x != -10 вы правильно вычисляете возможное значение x, равное -16, но которое не входит в ОДЗ. А проверить уравнение на значение x=-10 забыли. В этом случае обе части уравнения обращаются в 0, т.к. log_11 (11+x) = log_11 (1) = 0 Таким образом x = -10 является решением уравнения.
Ответ: x = -10
Неизвестный
04.06.2009, 13:39
общий
Мда! прокол вышел . Надеюсь, Nightwalker успеет прочитать ответы.
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