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end{aligned} Thus, we have conclusion (3.1).
Thus, by multiplying both sides by ln b − ln a 2 in (9), we have conclusion (8) immediately.
Using (2.10), the boundedness of and the Lagrange's mean-value theorem for the function,,, on if or if, we have conclusion (iii).
The alternative case, in which we have conclusion (ii) in Lemma 4.4, is proved the same way, using in place of.
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Then we have conclusions of Theorem 3.3.
Finally, we have conclusions in section 7.
Then we have conclusions (a) and (b) of Theorem 3.2.
"We hope to have a conclusion and announcement Friday morning".
Thus we have the conclusion.
Then we have the conclusion.
Therefore, we have the conclusion.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com