Вычислите логарифм [tex] log_{ \sqrt{2}+ \sqrt{1} }( \sqrt{2} - \sqrt{1})[/tex]. Created by kittycat13. algebra-ru

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kittycat13 @kittycat13

July 2022 1 6 Report

Вычислите логарифм [tex] log_{ \sqrt{2}+ \sqrt{1} }( \sqrt{2} - \sqrt{1})[/tex]

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NNNLLL54

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$\sqrt1=1\; \; \to$
$\sqrt2-1=\frac{(\sqrt2-1)(\sqrt2+1)}{\sqrt2+1}=\frac{2-1}{\sqrt2+1}=\frac{1}{\sqrt2+1}\\\\\log_{\sqrt2+1}{(\sqrt2-1)}=\log_{\sqrt2+1}\frac{1}{\sqrt2+1}=\\\\=\log_{\sqrt2+1}{(\sqrt2+1)^{-1}}=-\log_{\sqrt2+1}{(\sqrt2+1)}=-1$

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