[tex]\log_6\frac{\log_{25}5*\log_{36}6}{\log_464+\log_264}=\log_6\frac{\log_{25}\sqrt{25}*\log_{36}\sqrt{36}}{\log_44^3+\log_22^6}=\log_6\frac{\log_{25}25^{\frac{1}{2}}*\log_{36}36^{\frac{1}{2}}}{3\log_44+6\log_22}=\\\\=\log_6\frac{\frac{1}{2}\log_{25}25*\frac{1}{2}\log_{36}36}{3*1+6*1}=\log_6\frac{\frac{1}{2}*1*\frac{1}{2}*1}{3+6}=\log_6\frac{\frac{1}{4}}{9}=\log_6(\frac{1}{4}*\frac{1}{9})=\log_6(\frac{1}{36})=\\\\=\log_6(\frac{1}{6^2})=\log_66^{-2}=-2\log_66=-2*1=-2[/tex]
[tex]\frac{(\log_612+\log_63)*(\log_{\frac{1}{3}}4,5+\log_{\frac{1}{3}}2)}{\log_{0,5}0,125*\log_{0,5}4}=\frac{\log_6(12*3)*\log_{\frac{1}{3}}(4,5*2)}{\log_{\frac{1}{2}}\frac{1}{8}*\log_{\frac{1}{2}}4}=\frac{\log_636*\log_{\frac{1}{3}}9}{\log_{\frac{1}{2}}(\frac{1}{2})^3*\log_{\frac{1}{2}}(\frac{1}{2})^{-2}}=[/tex]
[tex]\\\\=\frac{\log_66^2*\log_{\frac{1}{3}}(\frac{1}{3})^{-2}}{3\log_{\frac{1}{2}}\frac{1}{2}*(-2)*\log_{\frac{1}{2}}\frac{1}{2}}=\frac{2\log_66*(-2)*\log_{\frac{1}{3}}\frac{1}{3}}{3*1*(-2)*1}=\frac{2*1*(-2)*1}{-6}=\frac{-4}{-6}=\frac{2}{3}[/tex]
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[tex]\log_6\frac{\log_{25}5*\log_{36}6}{\log_464+\log_264}=\log_6\frac{\log_{25}\sqrt{25}*\log_{36}\sqrt{36}}{\log_44^3+\log_22^6}=\log_6\frac{\log_{25}25^{\frac{1}{2}}*\log_{36}36^{\frac{1}{2}}}{3\log_44+6\log_22}=\\\\=\log_6\frac{\frac{1}{2}\log_{25}25*\frac{1}{2}\log_{36}36}{3*1+6*1}=\log_6\frac{\frac{1}{2}*1*\frac{1}{2}*1}{3+6}=\log_6\frac{\frac{1}{4}}{9}=\log_6(\frac{1}{4}*\frac{1}{9})=\log_6(\frac{1}{36})=\\\\=\log_6(\frac{1}{6^2})=\log_66^{-2}=-2\log_66=-2*1=-2[/tex]
[tex]\frac{(\log_612+\log_63)*(\log_{\frac{1}{3}}4,5+\log_{\frac{1}{3}}2)}{\log_{0,5}0,125*\log_{0,5}4}=\frac{\log_6(12*3)*\log_{\frac{1}{3}}(4,5*2)}{\log_{\frac{1}{2}}\frac{1}{8}*\log_{\frac{1}{2}}4}=\frac{\log_636*\log_{\frac{1}{3}}9}{\log_{\frac{1}{2}}(\frac{1}{2})^3*\log_{\frac{1}{2}}(\frac{1}{2})^{-2}}=[/tex]
[tex]\\\\=\frac{\log_66^2*\log_{\frac{1}{3}}(\frac{1}{3})^{-2}}{3\log_{\frac{1}{2}}\frac{1}{2}*(-2)*\log_{\frac{1}{2}}\frac{1}{2}}=\frac{2\log_66*(-2)*\log_{\frac{1}{3}}\frac{1}{3}}{3*1*(-2)*1}=\frac{2*1*(-2)*1}{-6}=\frac{-4}{-6}=\frac{2}{3}[/tex]