log 3√b b/3√a+3/log 3 √ab (a√b) +2loga √b. Created by Fiorella. algebra-ru

log 3 √ab (a√b) +2loga √b...

Fiorella @Fiorella

July 2022 1 9 Report

log 3√b b/3√a+3/log 3 √ab (a√b) +2loga √b

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$log_{b}a=2\\\\\log_{\sqrt[3]{b}}\frac{b}{\sqrt[3]{a}}- \frac{3}{\log_{\sqrt[3]{ab}}(a\sqrt{b})} +2\log_{a}\sqrt{b}=\\\\=3\log_{b}\left (b\cdot a^{-\frac{1}{3}}\right )-\frac{3}{3\log_{ab}(a\cdot b^{\frac{1}{2}})}+2\log_{a}b^{\frac{1}{2}}=\\\\=3\Big (1-\frac{1}{3}\log_{b}a\Big )- \frac{\log_{b}(ab)}{\log_{b}(a\cdot b^{\frac{1}{2}})} +2\cdot \frac{1}{2}\cdot \log_{a}b=\\\\=3-\log_{b}a- \frac{\log_{b}a+1}{\log_{b}a+\frac{1}{2}\log_{b}b} + \frac{1}{\log_{b}a} =$

$=3-2- \frac{2+1}{2+\frac{1}{2}} +\frac{1}{2}=\frac{3}{2}-\frac{3}{5/2}=\frac{3}{2}-\frac{6}{5}=\frac{15-12}{10}=\frac{3}{10}=0,3$

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