Cho $a,b,c$ là các số thực khác $0$ thỏa mãn...

Đặt , .
$\Rightarrow \left\{ \begin{matrix}
a={{\log }_{6}}t=\dfrac{1}{{{\log }_{t}}6} \\
b={{\log }_{9}}t=\dfrac{1}{{{\log }_{t}}9} \\
c={{\log }_{24}}t=\dfrac{1}{{{\log }_{t}}24} \\
\end{matrix} \right.$$\Rightarrow T=\dfrac{a}{b}+\dfrac{a}{c}=a\left( \dfrac{1}{b}+\dfrac{1}{c} \right)=\dfrac{1}{{{\log }_{t}}6}\left( {{\log }_{t}}9+{{\log }_{t}}24 \right)\Leftrightarrow T=\dfrac{1}{{{\log }_{t}}6}.\left( {{\log }_{t}}216 \right)=\dfrac{1}{{{\log }_{t}}6}.\left( {{\log }_{t}}{{6}^{3}} \right)=3T=3$.