a=b^\frac53;\\
a\cdot b=a\cdot a^\frac35=a^{1+\frac35}=a^\frac85;\\
a\cdot b^3=a\cdot a^{3\cdot\frac35}=a\cdot a^{\frac{9}{5}}=a^{1+\frac95}=\\
=a^\frac{14}{5};\\
\log_{ab}(ab^3)=\log_{a^\frac85}\left(a^{\frac{14}{5}}\right)=\\
=\frac{\frac{14}{5}}{\frac{8}{5}}\log_aa=\frac{\frac{14}{5}}{\frac{8}{5}}=\frac{14}{8}=\frac74=1\frac34=1,75" alt="\log_ab=0,6;\\
\log_{ab}(ab^3)-?\\
\log_ab=\frac35;\\
a^{\log_ab}=a^{\frac35};\\
b=a^\frac35;<==>a=b^\frac53;\\
a\cdot b=a\cdot a^\frac35=a^{1+\frac35}=a^\frac85;\\
a\cdot b^3=a\cdot a^{3\cdot\frac35}=a\cdot a^{\frac{9}{5}}=a^{1+\frac95}=\\
=a^\frac{14}{5};\\
\log_{ab}(ab^3)=\log_{a^\frac85}\left(a^{\frac{14}{5}}\right)=\\
=\frac{\frac{14}{5}}{\frac{8}{5}}\log_aa=\frac{\frac{14}{5}}{\frac{8}{5}}=\frac{14}{8}=\frac74=1\frac34=1,75" align="absmiddle" class="latex-formula">