А знаете ли вы, что... Гриб-шампиньон вырастает всего за 72 часа. (видео)

Логарифмы - Бревнорифмы или не такая уж и скучная математика


Приветствую всех на моей первой записи в блоге. О чем же я собираюсь тут писать? Я собираюсь писать тут о математике и физике. Для начала хотел бы задать вопрос: Можно ли понимать математику, если ты ее не любишь? Думаю, что нет. Поэтому я создаю этот блог, чтобы показать, что математика - это очень даже интересно!(только предупреждаю, лучше все-таки читать учебники и ходить на уроки Smile )

Я думаю, мало кому интересно будет разжевывание материала 1-7 класса. Поэтому я сразу перейду к более интересным вещам, а именно - к логарифмам! Я думаю, что они идеально подойдут для первой записи в блоге: нетрудная и интересная тема. А еще смешная, ведь сокращение "log"
можно перевести с английского как "Бревно"
Ладно, начинаем:
Логарифм числа b по основанию a обозначается так:

Что же такое логарифм? Из написанного видно, что это степень. Если логарифм числа b по основанию a равен c, то это значит, что если a возвести в степень c, то получится b.
А если логарифм - это степень, то мы можем сделать такую вот интересную запись:

С другой стороны, b - это a возведенное в степень c(на рисунке я зачем-то поставил вместо c n), значит, мы можем записать логарифм вот так:

А теперь вопрос: что будет, если мы совместим запись (1) и (2)?
Вот ответ: выглядит забавно, не правда ли?

Думаю, такая интересная и необычная "бесконечная" запись уже развеяла весь страх читателя(если только он уже не был с данной темой) пред словом "логарифм".

А теперь перейдем к свойствам логарифмов. В этой записи я разберу только одно свойство, остальные разберу позже.
Итак, давайте докажем следующее свойство:

Я приведу здесь два доказательства: полуинтуитивное(т.е. как я для себя это понимаю) и нормальное математическое доказательство, какое приводится в учебниках.

Полуинтуитивное доказательство Пусть логарифм b по основанию а равен n, а логарифм c по основанию a равен m. Мы знаем, что в таком случае b = a^n(значок ^ обозначает возведение в степень), а c = a^m. А еще мы знаем, что логарифм - это степень. А степени складываются при произведении результатов возведения в степень(прошу прощения, если что непонятно). А b(или a^n) и c(или а^m) и есть результаты возведения в степень. Отсюда

Математическое доказательство Пусть

а

Мы знаем, что

Теперь заменим b на a^x, а c на a^y. После некоторых преобразований заменим x и y на log b по основанию a и log c по основанию a соответственно:

Убирая все промежуточные преобразования, получаем

Что и требовалось доказать!

На этом пока все, удачи и до следующих записей!

Комментарии
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mcseemprime, Пн, 11/03/2013 - 17:17

Ух! Надо понять

мухин дмитрий, Вс, 10/03/2013 - 08:01

очень прикольный блог. мне очень понравилось

BlueDog, Сб, 16/02/2013 - 23:26

Рад, что Вам понравилось.
Ну, раз отзывы по первой статье положительные, буду готовить вторую часть.

Олег Вдовиченко, Сб, 16/02/2013 - 22:06

Отличное разъяснение!

BlueDog, Пт, 15/02/2013 - 22:50

Спасибо Smile

Smeet007, Пт, 15/02/2013 - 22:47

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BlueDog, Пт, 15/02/2013 - 17:35

Просьба указывать на ошибки, давать отзывы и задавать вопросы.

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