\(log_{ab}a^2=3\)
=>\(\dfrac{1}{log_{a^2}ab}=\dfrac{1}{3}\)
=>\(\dfrac{1}{\dfrac{1}{2}\cdot log_aab}=\dfrac{1}{3}\)
=>\(\dfrac{2}{log_aa+log_ab}=\dfrac{1}{3}\)
=>\(\dfrac{2}{1+log_ab}=\dfrac{1}{3}\)
=>\(1+log_ab=6\)
=>\(log_ab=5\)
\(T=log_{ab}\left(\sqrt[3]{\dfrac{a}{b}}\right)\)
\(=\dfrac{1}{3}\cdot log_{ab}\left(\dfrac{a}{b}\right)\)
\(=\dfrac{1}{3}\cdot log_{ab}\left(\dfrac{a^2}{ab}\right)\)
\(=\dfrac{1}{3}\left(log_{ab}a^2-1\right)\)
\(=\dfrac{1}{3}\left(3-1\right)=\dfrac{1}{3}\cdot2=\dfrac{2}{3}\)
=>Chọn D