Oblicz a) [latex]log_{9} (log_{8}(log 100)) [/latex] b) [latex]log_{8}(log_{ frac{1}{4} }(log sqrt{10})) [/latex]

[latex]log_{9}(log_{8}(log 100))=log_{9}(log_{8}(log 10^2))=log_{9}(log_{8}(2log 10))=log_{9}(log_{8} 2)=\ log_{9}(log_{8} 8^frac{1}{3})=log_{9}dfrac{1}{3}=log_{9}dfrac{1}{9^frac{1}{2}}=log_{9} 9^{-frac{1}{2}}=-dfrac{1}{2}[/latex] --- [latex]log_{8}(log_frac{1}{4}(logsqrt{10}))=log_{8}(log_frac{1}{4}(log10^frac{1}{2}))=log_{8}(log_frac{1}{4}dfrac{1}{2})=log_{8}(log_frac{1}{4}(dfrac{1}{4})^frac{1}{2})=log_{8} dfrac{1}{2}=log_{8} dfrac{1}{8^frac{1}{3}}=log_{8} 8^{-frac{1}{3}}=-dfrac{1}{3}[/latex]