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## Main Question or Discussion Point

I am looking at examples of Maclaurin expansions for different functions, such as e^x, and sinx. But there is no expansion for log(x), only log(x+1). Why is that?

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- Thread starter Mr Davis 97
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I am looking at examples of Maclaurin expansions for different functions, such as e^x, and sinx. But there is no expansion for log(x), only log(x+1). Why is that?

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FactChecker

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So why does it have log(x+1), and not log(x+1/2) or log(x+2), for example?

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Mark44

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Mostly convenience, I suppose. Each of the other two expressions could also be expanded as Maclaurin series.So why does it have log(x+1), and not log(x+1/2) or log(x+2), for example?

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mathman

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Log((x+1)/(x-1)) gives a series that can be used for any y=(x+1)/(x-1)

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FactChecker

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Expanding the Maclaurin series at x=0 would be trying to evaluate the log at negative numbers.Log((x+1)/(x-1)) gives a series that can be used for any y=(x+1)/(x-1)

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mathman

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MacLaurin series at x = 0 has minus infinity as the constant term.

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