LOGARYTMY!! Bardzo pilne! Oblicz: [latex](log_sqrt{7} [/latex][latex]6 + log_{sqrt{7}}[/latex][latex]frac{1}{42} ) ( log_{frac{1}{2}} 1frac{1}{8} - log_{frac{1}{2}} 9 ) [/latex]                  

Korzystamy z definicji i własności logarytmu:   [latex]log_{a}b=c iff a^{c}=b[/latex] [latex]log_{a}b+log_{a}c=log_{a}(b*c)\log_{a}b-log_{a}c=log_{a}(b:c)[/latex]     [latex](log_{sqrt{7}}6+log_{sqrt{7}}frac{1}{42})*(log_{frac{1}{2}}1frac{1}{8}-log_{frac{1}{2}}9)=\\(log_{sqrt{7}}(6*frac{1}{42}))*(log_{frac{1}{2}}(1frac{1}{8}:9))=log_{sqrt{7}}frac{6}{42}*log_{frac{1}{2}}(frac{9}{8}*frac{1}{9})=\\log_{sqrt{7}}frac{1}{7}*log_{frac{1}{2}}frac{1}{8}=-2*3=-6\\\Objasnienia:\ o log_{sqrt{7}}frac{1}{7}=-2, bo sqrt{7}^{-2}=(7^{frac{1}{2}})^{-2}=7^{-1}=frac{1}{7}\\ o log_frac{1}{2}frac{1}{8}=3, bo (frac{1}{2})^{3}=frac{1}{8}[/latex]