abcdefghijklmnopqrstu's blog

Вопрос про логарифмы
By abcdefghijklmnopqrstu, 11 years ago, translation, In English

Hello! I have a question: how to find value of , if we know value of and we shouldnt find x, because it may be very-very big? Is it impossible?

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11 years ago, # |
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UPD: Это разные функции, но ничего. Уверен, они дают повод для размышлений.

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11 years ago, # |
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for very large x.

Of course, if x is very-very big, then up to precision of your data types, the difference is negligible (if is in the order of 103, is in the order of 10 - 400) and you can just write .

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    11 years ago, # ^ |
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    It can be shown that error is asymptotically small enough.

    (Mean value theorem)

    Thus if x if large enough you may say that and get the error of order not more than O(1 / x2).

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    11 years ago, # ^ |
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    Actually you could take first k elements of Taylor series and precision will be

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