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working on Prime Number Theorem and the book gives an equality that I probably should know...

[itex]\frac{1}{log(2x)}= \frac{1}{logx}- \frac{log2}{log^{2}x} + O(\frac{1}{log^{3}x})[/itex]

and

[itex]\frac{1}{log^{2}2x} = \frac{1}{log^{2}x} + O(\frac{1}{log^{3}x}) [/itex]

Not sure what kind of expansion or what lets them draw this conclusion.

Any help is appreciated!

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# Log expansion

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