a= \sqrt[4]{3 \sqrt[3]{3 \sqrt{3 \sqrt[2]{3} } } }=
=3^{\frac{1}{4}}*(3^{\frac{1}{3}})^{\frac{1}{4}}*((3^{\frac{1}{2}})^{\frac{1}{3}})^{\frac{1}{4}}*(((3^{\frac{1}{2}})^{\frac{1}{2}})^{\frac{1}{3}})^{\frac{1}{4}}=
=3^{\frac{1}{4}}*3^{\frac{1}{12}}*3^{\frac{1}{24}}*3^{\frac{1}{48}}=3^{\frac{12+4+2+1}{48}}=3^{\frac{19}{48}}
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b=9 \sqrt{27} * 3^{-2,5} *( \frac{1}{3} ) ^{ \frac{1}{4} } *( \frac{1}{81} ) ^{- \frac{2}{3} }=
=3^2*(3^3)^{\frac{1}{2}}*3^{-\frac{5}{2}}*3^{-\frac{1}{4}}*(3^4)^{\frac{2}{3}}=
=3^2*3^{\frac{3}{2}}*3^{-\frac{5}{2}}*3^{-\frac{1}{4}}*3^{\frac{8}{3}}=
=3^{\frac{24+18-30-3+32}{4}}=3^{\frac{41}{12}}
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a=3^{\frac{19}{48}} , b=3^{\frac{41}{12}}
log_{3^{\frac{19}{48}}}(3^{\frac{41}{12}})=x
(3^{\frac{19}{48}})^x=3^{\frac{41}{12}}
3^{\frac{19}{48}x}=3^{\frac{164}{48}}
\frac{19}{48}x=\frac{164}{48} \ |*48
19x=164
x=\frac{164}{19}
log_ab=log_{3^{\frac{19}{48}}}(3^{\frac{41}{12}})=\frac{164}{19}